Intermediate Algebra: Connecting Concepts through Applications

Problem 1

Solve each equation. Check each answer.
$$
2 x+10=40
$$

Erika Bustos

Numerade Educator

Problem 2

Solve each equation. Check each answer.
$$
3 x+14=35
$$

Erika Bustos

Numerade Educator

00:25

Problem 3

Solve each equation. Check each answer.
$$
-4 t+8=-32
$$

Erika Bustos

Numerade Educator

00:21

Problem 4

Solve each equation. Check each answer.
$$
-7 m+20=48
$$

Erika Bustos

Numerade Educator

00:32

Problem 5

Solve each equation. Check each answer.
$$
2.5 x+7.5=32.5
$$

Erika Bustos

Numerade Educator

00:39

Problem 6

Solve each equation. Check each answer.
$$
3.4 x-8.2=15.6
$$

Erika Bustos

Numerade Educator

00:37

Problem 7

Solve each equation. Check each answer.
$$
20=5.2 x-0.8
$$

Erika Bustos

Numerade Educator

00:32

Problem 8

Solve each equation. Check each answer.
$$
45=-3.6 c+189
$$

Erika Bustos

Numerade Educator

00:55

Problem 9

Solve each equation. Check each answer.
$$
0.05(x-200)=240
$$

Erika Bustos

Numerade Educator

00:59

Problem 10

Solve each equation. Check each answer.
$$
0.03(n-500)=108
$$

Erika Bustos

Numerade Educator

00:51

During the first day of training on the job, a new candy maker gets faster at making candies. The number of candies a new employee can produce during an hour can be represented by $C=10 h+20$ candies, where $h$ is the number of hours of training.
a. Find the number of candies a new employee can produce in an hour after 1 hour of training.
b. Find the number of candies a new employee can produce in an hour after 4 hours of training.
c. How many hours of training must an employee receive before being able to produce 150 candies an hour?

Erika Bustos

Numerade Educator

Problem 12

The number of students who are enrolled in math classes at a local college can be represented by $E=-17 w+600$ where $E$ represents the math class enrollment at the college $w$ weeks after the start of the fall semester.
a. Find the total enrollment in math classes at the college at the beginning of the fall semester. (Hint: Because the semester is just starting, $w=0 .)$
b. During which week will the total enrollment be 430 students?
c. What will the total enrollment be in math classes after 8 weeks?

Allison Knapp

Numerade Educator

01:54

Problem 13

The estimated number of Amazon Prime members
in millions, $P,$ in the United States $q$ quarters since March 2015 can be represented by the equation
$$
P=7.89 q+33.73 .
$$
a. Find the estimated number of Amazon Prime members in the U.S. in March of 2017. (March 2017 is 8 quarters, 2 years, since March $2015 .$
b. Find the estimated number of Amazon Prime members in the U.S. in March of 2020
c. In what quarter will the estimated number of Amazon Prime members in the U.S. be 133 million?

Erika Bustos

Numerade Educator

01:12

Problem 14

The gasoline prices in Southern California can increase very quickly during the summer months. The equation $p=2.399+0.3 w$ represents the gasoline prices $p$ in dollars per gallon $w$ weeks after the beginning of summer.
a. What does gasoline cost after 5 weeks of summer?
b. During what week of summer will gasoline cost \$2.759 per gallon?

Erika Bustos

Numerade Educator

01:11

Problem 15

$P=1.5 t-300$ represents the profit in dollars from selling $t$ printed T-shirts.
a. Find the profit if you sell 100 printed T-shirts.
b. Find the profit if you sell 400 printed T-shirts.
c. How many printed T-shirts must you sell to make $\$ 1000$ in profit?

Erika Bustos

Numerade Educator

01:47

Problem 16

$P=5.5 b-500.5$ represents the profit in dollars from selling $b$ books.
a. Find the profit if you sell 75 books.
b. Find the profit if you sell 200 books.
c. How many books must you sell to make $\$ 3600$ in profit?

Erika Bustos

Numerade Educator

01:01

Problem 17

The total cost, $C,$ in dollars for a taxi ride in New York City can be represented by the equation
$$
C=2.50+2.0 m
$$
when the trip is $m$ miles long.
a. Determine the cost for a 25 -mile taxi ride in New York City.
b. How many miles can you ride in a New York City taxi for $\$ 100 ?$

Erika Bustos

Numerade Educator

01:05

Problem 18

A team of engineers is trying to pump out the air in a vacuum chamber to lower the pressure. They know that the following equation represents the pressure in the chamber:
$$
P=35-0.07 s
$$
where $P$ is the pressure in pounds per square inch (psi) of the vacuum chamber and $s$ is the time in seconds.
a. What will the pressure be after 150 seconds?
b. When will the pressure inside the chamber be 1 psi?

Erika Bustos

Numerade Educator

00:35

Problem 19

Determine which given value seems the most reasonable for the given situation. Explain why the other given values do not make sense in that situation.
$P$ is the population of Kentucky in thousands of people.
a. $P=3.5$
b. $P=4200$
c. $P=-210$

Erika Bustos

Numerade Educator

00:23

Problem 20

Determine which given value seems the most reasonable for the given situation. Explain why the other given values do not make sense in that situation.
$R$ is the revenue in dollars from selling kettle corn at a 2 -day rodeo.
a. $R=20$
b. $R=-3000$
c. $R=4500$

Erika Bustos

Numerade Educator

00:19

Problem 21

Determine which given value seems the most reasonable for the given situation. Explain why the other given values do not make sense in that situation.
$T$ is the temperature in degrees Fahrenheit at the South Pole.
a. $T=-50$
b. $T=75$
c. $T=82$

Erika Bustos

Numerade Educator

00:26

Problem 22

Determine which given value seems the most reasonable for the given situation. Explain why the other given values do not make sense in that situation.
$S$ is a cook's monthly salary in dollars from working at White Castle Hamburgers.
a. $S=10.50$
b. $S=1600$
c. $S=28,000$

Erika Bustos

Numerade Educator

01:46

Problem 23

Salespeople often work for commissions on the sales that they make for the company. As a new salesperson at a local technology company, you are told that you will receive an $8 \%$ commission on all sales you make after the first $\$ 1000$. Your pay can be represented by $p=0.08(s-1000)$ dollars, where $s$ is the amount of sales you make in dollars.
a. How much total pay will you earn from $\$ 2000$ in sales?
b. How much total pay will you earn from $\$ 50,000$ in sales?
c. If you need at least $\$ 500$ per week to pay your bills, what sales do you have to make per week?

Erika Bustos

Numerade Educator

01:23

Problem 24

At a new job selling high-end clothing to women, you earn $6 \%$ commission on all sales you make after the first $\$ 500$. Your pay can be represented by $p=0.06(s-500)$ dollars, where $s$ is the amount of sales you make in dollars.
a. How much total pay will you earn from $\$ 2000$ in sales?
b. How much total pay will you earn from $\$ 5000$ in sales?
c. If you need at least $\$ 450$ per week to pay your bills, what sales do you have to make per week?

Erika Bustos

Numerade Educator

02:08

Problem 25

Budget charges $\$ 29.95$ for the day and $\$ 0.55$ per mile driven to rent a 10 -foot moving truck.
a. Let $B$ be the cost of renting a 10 -foot moving truck from Budget for a day and driving the truck $m$ miles. Write an equation for the cost of renting from Budget.
b. How much would it cost to rent a 10 -foot truck from Budget if you were to drive it 75 miles?
c. How many miles could you drive the truck if you could pay only $\$ 100$ for the rental?

Melissa Bird

Numerade Educator

02:05

Problem 26

A local fitness club has a no-contract basic membership plan with an initiation fee of $\$ 59.99$ and a per month charge of $\$ 29.99 .$
a. Write an equation for the total cost, $C$, in dollars of this plan if you continue your membership for $m$ months.
b. Use your equation to determine the total cost of this membership for the first 2 years.
c. How many months of membership will $\$ 1000$ purchase at this club?

Alison Rodriguez

Numerade Educator

Problem 27

A salesperson is guaranteed $\$ 250$ per week plus a $7 \%$ commission on the total dollar value of all sales made.
a. Write an equation for your total pay per week, $P$, if you make $s$ dollars of sales.
b. What will your total pay be if you have sales of $\$ 2000 ?$
c. How many dollars of sales do you need to make to have a total weekly pay of $\$ 650 ?$

Alison Rodriguez

Numerade Educator

01:41

Problem 28

A salesperson is guaranteed $\$ 300$ per week plus a $5 \%$ commission on the total dollar value of all sales made.
a. Write an equation for your total pay per week, $P$, if you make $s$ dollars of sales.
b. What will your total pay be if you have sales of $\$ 4000 ?$
c. How many dollars of sales do you need to make to have a total weekly pay of $\$ 750 ?$

Alison Rodriguez

Numerade Educator

02:09

Problem 29

You are planning a trip to Las Vegas and want to calculate your expected costs for the trip. You found that you can take a tour bus trip for up to 7 days, and it will cost you $\$ 225$ for the round trip. You figure that you can stay at a hotel and eat for about $\$ 150$ per day.
a. Write an equation for the total cost of this trip depending on the number of days you stay. (We will ignore the gambling budget.)
b. How much will it cost for a 3 -day trip?
c. If you have $\$ 1200$ and want to gamble half of it, how many days can you stay in Las Vegas, assuming that you do not win any money?

Alison Rodriguez

Numerade Educator

01:38

Problem 30

Your family is planning a trip to Orlando, Florida, to visit the amusement parks. You want to budget for your expected costs. You find round trip flights for your four-person family that total $\$ 1600 .$ You expect the hotel, food, and admissions to cost about $\$ 900$ per day.
a. Write an equation for the total cost of this trip depending on the number of days you stay.
b. How much will it cost for a 5 -day trip?
c. If your family can afford to spend $\$ 7500$ on this trip, how many days can you stay in Orlando?

Alison Rodriguez

Numerade Educator

02:09

Problem 31

A professional photographer has several costs involved in taking pictures at an event such as a wedding. Editing and printing proofs of the photos cost $\$ 5.29$ each. The photographer also has to pay salaries of $\$ 800$ for the day.
a. Write an equation for the total cost to shoot a wedding depending on the number of proofs the photographer edits and prints.
b. How much will it cost the photographer if she edits and prints 100 proofs?
c. How many proofs can the photographer edit and print if the total cost cannot exceed a budget of $\$ 1750 ?$

Alison Rodriguez

Numerade Educator

View

Problem 32

The photographer from Exercise 31 charges her clients a $\$ 7.50$ fee for each proof she edits and prints plus a flat fee of $\$ 600$ for the wedding.
a. Write an equation for the total revenue for shooting the wedding depending on the number of proofs she edits and prints.
b. How much will the photographer charge the client for a wedding that she edits and prints 100 proofs for?
c. Write an equation for the profit made by the photographer depending on the number of proofs she edits and prints.
d. How much profit will the photographer make on a wedding if she edits and prints 100 proofs?
e. How many photos must the photographer edit and print to break even? (Breaking even means that profit $=0 .)$

Donna Densmore

Numerade Educator

02:14

Problem 33

A snow cone vendor on the Virginia Beach boardwalk has several costs of doing business. She pays salaries of $\$ 2000$ per month and other fixed costs, such as utilities and kiosk rental, of $\$ 1150$ per month. Each snow cone sold costs her 36 cents.
a. Write an equation for the total cost of selling snow cones for a month depending on the number of snow cones sold.
b. What will the monthly cost be if she sells 3000 snow cones in a month?
c. How many snow cones can she sell if the total monthly cost cannot exceed a budget of $\$ 4400 ?$

Alison Rodriguez

Numerade Educator

07:27

Problem 34

The snow cone vendor from Exercise 33 charges $\$ 2.50$
per snow cone.
a. Write an equation for the total revenue from selling snow cones for a month, depending on the number of snow cones sold.
b. How much revenue will the vendor make if she sells 3000 snow cones in a month?
c. Write an equation for the profit made by the snow cone vendor depending on the number of snow cones sold
d. How much profit will the vendor make from selling 4500 snow cones?
e. How many snow cones must the vendor sell in a month to break even? (Breaking even means that profit $=0 .$

Kelly Korek

Numerade Educator

01:31

Problem 35

The Squeaky Clean Window Cleaning Company has several costs included in cleaning windows for a business. The materials and cleaning solutions cost about $\$ 1.50$ per window. Insurance and salaries for the day will cost about $\$ 530 .$
a. Write an equation for the total cost to clean windows for a day depending on the number of windows cleaned.
b. How much will it cost if the company cleans 60 windows?
c. How many windows can the company clean if the total cost cannot exceed a budget of $\$ 800 ?$

Alison Rodriguez

Numerade Educator

03:46

Problem 36

The Squeaky Clean Window Cleaning Company from Exercise 35 charges companies $\$ 9$ per window cleaned plus a travel charge of $\$ 50$.
a. Write an equation for the total revenue for cleaning windows at a business depending on the number of windows cleaned.
b. How much will the Squeaky Clean Window Cleaning Company charge a business to clean 50 windows?
c. Write an equation for the profit made by the Squeaky Clean Window Cleaning Company depending on the number of windows cleaned.
d. How much profit will the company make from cleaning 80 windows for a business?
e. How many windows must the company clean in a day to break even? (Breaking even means that profit $=0 .$

Jenifer Roberts

Numerade Educator

01:08

Problem 37

Compare the two students' work to determine which student did the work correctly. Explain what mistake the other student made.
A small publicity company will custom-label water bottles for your company or event. It costs the publicity company $\$ 75$ to set up the label design and 55 cents for each bottle and custom label. Write an equation for the cost of each order depending on the number of bottles ordered.
$$
\begin{array}{|c|c|}
\hline \text { Javier } & \text { Maria } \\
C=\begin{array}{c}
\text { Cost of each } \\
\text { order in dollars }
\end{array} & \begin{array}{c}
C=\text { Cost of each } \\
\text { order in dollars }
\end{array} \\
b=\begin{array}{c}
\text { number of } \\
\text { bottles ordered } \\
C=75+55 b
\end{array} & \begin{array}{c}
b=\text { number of } \\
\text { bottles ordered }
\end{array} \\
C=75+0.55 b
\end{array}
$$

Jerelyn Nevil

Numerade Educator

02:21

Problem 38

Compare the two students' work to determine which student did the work correctly. Explain what mistake the other student made.
The same publicity company as in Exercise 37 has the following revenue equation:
$$
R=0.95 b
$$
where $R$ is the revenue in dollars from an order of $b$ custom-labeled bottles of water. Write an equation for the profit the publicity company will earn from an order of $b$ bottles
$$
\begin{array}{|c|c|}
\hline {\text { Rosemary }} & {\text { Will }} \\
P=\begin{array}{c}
\text { Profit of each order in } \\
\text { dollars }
\end{array} & \begin{array}{c}
P=\text { Profit of each order } \\
\text { in dollars }
\end{array} \\
\begin{array}{c}
b=\text { number of bottles } \\
\text { ordered }
\end{array} & \begin{array}{c}
b=\text { number of bottles } \\
\text { ordered }
\end{array} \\
P=0.95 b-(75+0.55 b) & P=0.95 b-75+0.55 b \\
P=0.95 b-75-0.55 b & P=-75+1.50 b \\
P=-75+0.40 b &
\end{array}
$$

Jerelyn Nevil

Numerade Educator

01:20

Problem 39

Enviro-Safe Pest Management charges new clients $\$ 150$ for an in-home inspection and initial treatment for ants. Monthly preplanned treatments cost $\$ 38$.
a. Write an equation for the total cost for pest management from Enviro-Safe Pest Management depending on the number of months a house is treated.
b. If the house has an initial treatment and then is treated monthly for 1.5 more years, how much will Enviro-Safe charge?

Alison Rodriguez

Numerade Educator

02:11

Problem 40

The population of the United States since 2010 can be estimated by the equation $P=2.76 t+309.37,$ where $P$ is the population in millions $t$ years since $2010 .$ Source: Based on data from the U.S. Census Bureau.
a. What was the population of the United States in $2013 ?$
b. In what year, was the population of the United States $326,000,000 ?$
c. In what year will the population of the United States reach 375 million?

Alison Rodriguez

Numerade Educator

02:48

Problem 41

A small manufacturer of golf clubs is concerned about monthly costs. The workshop costs $\$ 23,250$ per month to run in addition to the $\$ 145$ in materials per set of irons produced.
a. Write an equation for the monthly costs of this club manufacturer.
b. What are the monthly costs for this company if they make 100 sets of irons?
c. How many sets of irons does this manufacturer need to produce for their costs to be $\$ 20,000 ?$

Alison Rodriguez

Numerade Educator

02:11

Problem 42

You are in charge of creating and purchasing T-shirts for a local summer camp. After calling a local silkscreening company, you find that to purchase 100 or more T-shirts, there will be a $\$ 150$ setup fee and a $\$ 5$ charge per T-shirt.
a. Write an equation for the total cost, $C$, in dollars of making $t$ T-shirts.
b. How much would 300 T-shirts cost?
c. How many T-shirts can you purchase with a budget of $\$ 1500 ?$
d. If this camp wants to break even selling 300 T-shirts, what should they charge for each T-shirt?

Alison Rodriguez

Numerade Educator

02:38

Problem 43

Rockon, a small-town rock band, wants to produce a EP before their next summer concert series. They have looked into a local recording studio and found that it will cost them $\$ 1500$ to produce the master recording and then an additional $\$ 1.50$ to make each EP up to 500 .
a. Write an equation for the total cost, $C,$ in dollars of producing $n$ EPs.
b. How much will it cost Rockon to make 250 EPs?
c. If Rockon has $\$ 2000$ to produce EPs, how many can they order?
d. If Rockon has $\$ 3000$ to produce EPs, how many can they order?

Alison Rodriguez

Numerade Educator

01:27

Problem 44

The percent $P$ of companies that are still in business $t$ years after the fifth year in operation can be represented by the equation
$$
P=-3 t+50
$$
a. What percentage of companies are still in business after 1 year in operation?
b. What percentage of companies are still in business after 25 years in operation?
c. After how many years are there only $35 \%$ of companies still in business?

Erika Bustos

Numerade Educator

01:24

Problem 45

Use the information from Exercise 25 to answer the following questions.
a. If Budget doubled the cost per mile, how would that change the equation found in Exercise 25 part a?
b. Would the cost to drive 75 miles also double? Explain your reasoning.

Melissa Bird

Numerade Educator

02:36

Problem 46

Use the information from Exercise 26 to answer the following questions.
a. If the membership plan doubled the cost per month, how would that change the equation found in Exercise 26 part a?
b. Would the total cost for 2 years also double? Explain your reasoning.

Jerelyn Nevil

Numerade Educator

02:01

Problem 47

Use the information from Exercise 27 to answer the following questions.
a. If the salesperson is given a raise by increasing the guaranteed pay per week $\$ 100,$ how would that change the equation found in Exercise 27 part a?
b. If instead of raising the guaranteed pay per week, the salesperson's commission rate was increased from $7 \%$ to $8 \%$, how would that change the equation found in Exercise 27 part a?
c. If the salesperson makes an average of $\$ 7000$ in sales per week, which raise would be best for the salesperson?
d. If the salesperson makes an average of $\$ 4000$ in sales per week, which raise would be best for the company?
e. What amount of sales per week would make these raises result in the same weekly pay?

Joseph Palsic

Numerade Educator

02:17

Problem 48

Use the information from Exercise 28 to answer the following questions.
a. If the salesperson is given a raise by increasing the guaranteed pay per week $\$ 150,$ how would that change the equation found in Exercise 28 part a?
b. If instead of raising the guaranteed pay per week, the salesperson's commission rate was increased from $5 \%$ to $6 \%,$ how would that change the equation found in Exercise 27 part a?
c. If the salesperson makes an average of $\$ 20,000$ in sales per week, which raise would be best for the salesperson?
d. If the salesperson makes an average of $\$ 11,000$ in sales per week, which raise would be best for the company?
e. What amount of sales per week would make these raises result in the same weekly pay?

Joseph Palsic

Numerade Educator

01:12

Problem 49

Use the information from Exercises 31 and 32 to answer the following questions.
a. If the salaries the photographer has to pay increase by $50 \%,$ how does that change the cost equation?
b. How does the increase in salary affect the profit for the photographer?
c. If the photographer wants to cover the increase in salaries, how much should she increase the charge per proof if the client wants 100 proofs?

Joseph Palsic

Numerade Educator

00:55

Problem 50

Use the information from Exercises 33 and 34 to answer the following questions.
a. If the kiosk rental increases by $20 \%,$ how does that change the cost equation?
b. How does the increase in kiosk rent affect the profit for the snow cone vendor?
c. If the snow cone vendor wants to cover the increase in rent, how much should she increase the charge per snow cone if she can sell 6000 snow cones per month?

Joseph Palsic

Numerade Educator

01:25

Problem 51

Complete the table by filling in the missing algebraic steps to solve the equation or supply the missing reasons for those steps.
$$
3 x+10=8 x-15
$$
$$
\begin{array}{|c|l|}
\hline \begin{array}{c}
\text { Algebraic Step to } \\
\text { Solve the Equation }
\end{array} & \text { Reason for Each Step } \\
\hline \begin{array}{c}
3 x+10=8 x-15 \\
-8 x & -8 x
\end{array} & \\
\hline & \begin{array}{l}
\text { Isolate the variable term } \\
\text { by using the subtraction } \\
\text { property of equality. }
\end{array} \\
\hline \frac{-5 x}{-5}=\frac{-25}{-5} & \\
\hline & \text { The solution } \\
\hline
\end{array}
$$

Erika Bustos

Numerade Educator

01:07

Problem 52

Complete the table by filling in the missing algebraic steps to solve the equation or supply the missing reasons for those steps.
$$
-4 x+7=-8 x-9
$$
$$
\begin{array}{|c|l|}
\hline \begin{array}{c}
\text { Algebraic Step to } \\
\text { Solve the Equation }
\end{array} & {\text { Reason for Each Step }} \\
\hline & \begin{array}{l}
\text { Move the variable terms to } \\
\text { one side using the addition } \\
\text { property of equality. }
\end{array} \\
\hline 4 x+7=-9 & \\
-7 \quad-7 & \\
\hline & \begin{array}{l}
\text { Solve for the variable using the } \\
\text { division property of equality. }
\end{array} \\
\hline x=-4 & \\
\hline
\end{array}
$$

Erika Bustos

Numerade Educator

01:47

Problem 53

Complete the table by filling in the missing algebraic steps to solve the equation or supply the missing reasons for those steps.
$$
2(x-5)+7=-3 x+12
$$
$$
\begin{array}{|c|l|}
\hline \begin{array}{c}
\text { Algebraic Step to Solve the } \\
\text { Equation }
\end{array} & {\text { Reason for Each Step }} \\
\hline 2(x-5)+7=-3 x+12 & \\
2 x-10+7=-3 x+12 & \\
\hline & \begin{array}{l}
\text { Combine like terms on each } \\
\text { side of the equation. }
\end{array} \\
\hline \begin{array}{c}
2 x-3=-3 x+12 \\
+3 x & +3 x
\end{array} & \\
\hline & \begin{array}{l}
\text { Isolate the variable term using } \\
\text { the addition property of equality. }
\end{array} \\
\hline & \begin{array}{l}
\text { Solve for the variable using the } \\
\text { division property of equality. }
\end{array} \\
\hline x=3 & \\
\hline
\end{array}
$$

Alison Rodriguez

Numerade Educator

03:23

Problem 54

Complete the table by filling in the missing algebraic steps to solve the equation or supply the missing reasons for those steps.
$$
6 x+1=-2(2 x+1)-3
$$
$$
\begin{array}{|c|l|}
\hline \begin{array}{c}
\text { Algebraic Step to Solve } \\
\text { the Equation }
\end{array} & {\text { Reason for Each Step }} \\
\hline & \begin{array}{l}
\text { Simplify the right side } \\
\text { by using the distributive } \\
\text { property. }
\end{array} \\
\hline \begin{array}{l}
6 x+1=-4 x-2-3 \\
6 x+1=-4 x-5
\end{array} & \begin{array}{l}
\end{array} \\
\hline & \begin{array}{l} \text { Move the variable terms to } \\
\text { one side using the addition } \\
\text { property of equality. } \end{array} \\
\hline 10 x+1=-5 & \\
-1-1 & \\
\hline & \begin{array}{l}
\text { Solve for the variable } \\
\text { using the division property } \\
\text { of equality. }
\end{array} \\
\hline x=-\frac{6}{10}=-\frac{3}{5} & \\
\hline
\end{array}
$$

Emily Himsel

Numerade Educator

01:57

Problem 55

Solve each equation. Provide reasons for each step. Check the answer.
$$
5 x+60=2 x+90
$$

Alison Rodriguez

Numerade Educator

01:28

Problem 56

Solve each equation. Provide reasons for each step. Check the answer.
$$
6 x+20=9 x+5
$$

Alison Rodriguez

Numerade Educator

01:23

Problem 57

Solve each equation. Provide reasons for each step. Check the answer.
$$
\frac{2}{5} d+6=14
$$

Alison Rodriguez

Numerade Educator

02:10

Problem 58

Solve each equation. Provide reasons for each step. Check the answer.
$$
\frac{3}{4} x-17=20
$$

Alison Rodriguez

Numerade Educator

01:19

Problem 59

Solve each equation. Provide reasons for each step. Check the answer.
$$
\frac{1}{3} m+\frac{4}{3}=4
$$

Alison Rodriguez

Numerade Educator

01:06

Problem 60

Solve each equation. Provide reasons for each step. Check the answer.
$$
\frac{1}{2} x+\frac{3}{2}=5
$$

Alison Rodriguez

Numerade Educator

02:10

Problem 61

Solve each equation. Provide reasons for each step. Check the answer.
$$
-3 x-6=14+8 x
$$

Alison Rodriguez

Numerade Educator

02:16

Problem 62

Solve each equation. Provide reasons for each step. Check the answer.
$$
5 r-9=18 r+2
$$

Alison Rodriguez

Numerade Educator

01:48

Problem 63

Solve each equation. Provide reasons for each step. Check the answer.
$$
5 r-9=18 r+2
$$

Suzanne W.

Numerade Educator

04:29

Problem 64

Solve each equation. Provide reasons for each step. Check the answer.
$$
\frac{3}{8} p-\frac{4}{9}=\frac{5}{8} p+7
$$

Alison Rodriguez

Numerade Educator

02:13

Problem 65

Solve each equation. Check the answer.
$$
1.25 d-3.4=-2.3(5 d+4)
$$

Erika Bustos

Numerade Educator

02:07

Problem 66

Solve each equation. Check the answer.
$$
3.7 m-4.6=-1.8(6 m+8)
$$

Erika Bustos

Numerade Educator

01:14

Problem 67

Solve each equation. Check the answer.
$$
3(c+5)-21=107
$$

Erika Bustos

Numerade Educator

01:30

Problem 68

Solve each equation. Check the answer.
$$
5 k+7=2(6 k-14)+56
$$

Erika Bustos

Numerade Educator

01:31

Problem 69

Solve each equation. Check the answer.
$$
1.7 d+5.7=29.7+5 d
$$

Erika Bustos

Numerade Educator

02:03

Problem 70

Solve each equation. Check the answer.
$$
2.1 m+3.4=7.2-9.4 m
$$

Erika Bustos

Numerade Educator

Problem 71

Solve each equation. Check the answer.
$$
\frac{3}{7}(2 z-5)=\frac{4}{7}(-3 z+9)
$$

Erika Bustos

Numerade Educator

01:40

Problem 72

Solve each equation. Check the answer.
$$
\frac{2}{5}(3 r-8)=\frac{3}{5}(-4 r+6)
$$

Erika Bustos

Numerade Educator

01:53

Problem 73

Solve each equation. Check the answer.
$$
-3(2 v+9)-3(3 v-7)=4 v+6(2 v-8)
$$

Suzanne W.

Numerade Educator

03:55

Problem 74

Solve each equation. Check the answer.
$$
4(2 x+7)-6(4 x-8)=12 x+3(4 x-9)
$$

Suzanne W.

Numerade Educator

02:45

Problem 75

Solve each equation. Check the answer.
$$
-\frac{8}{9}(3 t+5)=\frac{2}{3} t-12
$$

Erika Bustos

Numerade Educator

02:29

Problem 76

Solve each equation. Check the answer.
$$
-\frac{2}{7}(4 x+2)=\frac{3}{28} x-15
$$

Erika Bustos

Numerade Educator

00:08

Problem 77

Solve for the indicated variable.
$$
\text { Force: } \quad F=m a \quad \text { for } a \text { . }
$$

Erika Bustos

Numerade Educator

00:08

Problem 78

Solve for the indicated variable.
$$
\text { Weight (newtons): } \quad W=m g \quad \text { for } m
$$

Erika Bustos

Numerade Educator

00:09

Problem 79

Solve for the indicated variable.
$$
\text { Impulse: } \quad J=F t \quad \text { for } F \text { . }
$$

Erika Bustos

Numerade Educator

00:08

Problem 80

Solve for the indicated variable.
$$
P=10 h \text { for } h
$$

Erika Bustos

Numerade Educator

00:20

Problem 81

Solve for the indicated variable.
$$
\text { Angular acceleration: } \omega=\omega_{0}+\alpha t \quad \text { for } \alpha
$$

Erika Bustos

Numerade Educator

00:19

Problem 82

Solve for the indicated variable.
$$
y=m x+b \quad \text { for } b
$$

James Kiss

Numerade Educator

Problem 83

Solve for the indicated variable.
$$
\text { Rotational kinetic energy }(\mathrm{J}): \quad K=\frac{1}{2} I \omega^{2} \quad \text { for } I
$$

Erika Bustos

Numerade Educator

Problem 84

Solve for the indicated variable.
$$
\text { Elastic potential energy }(\mathrm{J}): \quad U=\frac{1}{2} k x^{2} \quad \text { for } k
$$

Erika Bustos

Numerade Educator

00:17

Problem 85

Solve for the indicated variable.
$$
\text { Kinetic energy }(\mathrm{J}): \quad k=\frac{1}{2} m v^{2} \quad \text { for } m
$$

Erika Bustos

Numerade Educator

00:16

Problem 86

Solve for the indicated variable.
$$
y=\frac{1}{2} x z^{2} \quad \text { for } x
$$

Erika Bustos

Numerade Educator

Problem 87

Solve for the indicated variable.
$$
a x+b y=c \quad \text { for } y
$$

Alejandro Ruiz

Numerade Educator

Problem 88

Solve for the indicated variable.
$$
2 x-y=z \quad \text { for } x
$$

Erika Bustos

Numerade Educator

00:17

Problem 89

Solve for the indicated variable.
$$
a x+5=y \quad \text { for } x
$$

Erika Bustos

Numerade Educator

00:16

Problem 90

Solve for the indicated variable.
$$
4 m+n=p \quad \text { for } m
$$

Erika Bustos

Numerade Educator

00:20

Problem 91

Solve for the indicated variable.
$$
b=2 c+3 d \text { for } c
$$

Erika Bustos

Numerade Educator

Problem 92

Solve for the indicated variable.
$$
x=3 y+5 z \text { for } y
$$

Erika Bustos

Numerade Educator

Problem 93

Solve for the indicated variable.
$$
5 x^{2}+3 y=z \text { for } y
$$

Erika Bustos

Numerade Educator