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  • Intermediate Algebra
  • Equations, Inequalities, and Problem Solving

Intermediate Algebra

Jerome E. Kaufmann, Karen L. Schwitters

Chapter 2

Equations, Inequalities, and Problem Solving - all with Video Answers

Educators

Section 1

Solving First-Degree Equations

00:40

Problem 1

Solve each equation.
$$
3 x+4=16
$$

Bailey R.
Bailey R.
Numerade Educator
00:52

Problem 2

Solve each equation.
$$
4 x+2=22
$$

Bailey R.
Bailey R.
Numerade Educator
00:51

Problem 3

Solve each equation.
$$
5 x+1=-14
$$

Bailey R.
Bailey R.
Numerade Educator
00:50

Problem 4

Solve each equation.
$$
7 x+4=-31
$$

Bailey R.
Bailey R.
Numerade Educator
00:57

Problem 5

Solve each equation.
$$
-x-6=8
$$

Bailey R.
Bailey R.
Numerade Educator
00:53

Problem 6

Solve each equation.
$$
8-x=-2
$$

Bailey R.
Bailey R.
Numerade Educator
00:53

Problem 7

Solve each equation.
$$
4 y-3=21
$$

Bailey R.
Bailey R.
Numerade Educator
00:53

Problem 8

Solve each equation.
$$
6 y-7=41
$$

Bailey R.
Bailey R.
Numerade Educator
00:53

Problem 9

Solve each equation.
$$
3 x-4=-4
$$

Bailey R.
Bailey R.
Numerade Educator
00:56

Problem 10

Solve each equation.
$$
5 x+1=12
$$

Bailey R.
Bailey R.
Numerade Educator
00:48

Problem 11

Solve each equation.
$$
-4=2 x-6
$$

Bailey R.
Bailey R.
Numerade Educator
00:56

Problem 12

Solve each equation.
$$
-2=3 a-2
$$

Bailey R.
Bailey R.
Numerade Educator
01:14

Problem 13

Solve each equation.
$$
-6 y-4=16
$$

Bailey R.
Bailey R.
Numerade Educator
01:18

Problem 14

Solve each equation.
$$
-8 y-2=18
$$

Bailey R.
Bailey R.
Numerade Educator
00:49

Problem 15

Solve each equation.
$$
4 x-1=4 x+7
$$

Bailey R.
Bailey R.
Numerade Educator
01:20

Problem 16

Solve each equation.
$$
9 x-3=6 x+18
$$

Bailey R.
Bailey R.
Numerade Educator
01:34

Problem 17

Solve each equation.
$$
5 y+2=2 y-11
$$

Bailey R.
Bailey R.
Numerade Educator
00:52

Problem 18

Solve each equation.
$$
9 y+3=9 y-10
$$

Bailey R.
Bailey R.
Numerade Educator
01:18

Problem 19

Solve each equation.
$$
3 x+4=5 x-2
$$

Bailey R.
Bailey R.
Numerade Educator
01:20

Problem 20

Solve each equation.
$$
2 x-1=6 x+15
$$

Bailey R.
Bailey R.
Numerade Educator
01:02

Problem 21

Solve each equation.
$$
-7 a+6=-8 a+14
$$

Bailey R.
Bailey R.
Numerade Educator
01:15

Problem 22

Solve each equation.
$$
-6 a-4=-7 a+11
$$

Bailey R.
Bailey R.
Numerade Educator
01:45

Problem 23

Solve each equation.
$$
5 x+3-2 x=x-15
$$

Bailey R.
Bailey R.
Numerade Educator
01:38

Problem 24

Solve each equation.
$$
4 x-2-x=5 x+10
$$

Bailey R.
Bailey R.
Numerade Educator
01:57

Problem 25

Solve each equation.
$$
6 y+18+y=2 y+3
$$

Debasish D.
Debasish D.
Numerade Educator
01:47

Problem 26

Solve each equation.
$$
5 y+14+y=3 y-7
$$

Debasish D.
Debasish D.
Numerade Educator
01:36

Problem 27

Solve each equation.
$$
4 x-3+2 x=8 x-3-x
$$

Debasish D.
Debasish D.
Numerade Educator
01:37

Problem 28

Solve each equation.
$$
x-4-4 x=6 x+9-8 x
$$

Debasish D.
Debasish D.
Numerade Educator
01:52

Problem 29

Solve each equation.
$$
6 n-4-3 n=3 n-4
$$

Debasish D.
Debasish D.
Numerade Educator
01:52

Problem 30

Solve each equation.
$$
2 n-1-3 n=5 n-7-3 n
$$

Debasish D.
Debasish D.
Numerade Educator
01:16

Problem 31

Solve each equation.
$$
4(x-3)=-20
$$

Debasish D.
Debasish D.
Numerade Educator
01:38

Problem 32

Solve each equation.
$$
3(x+2)=3 x+6
$$

Debasish D.
Debasish D.
Numerade Educator
01:18

Problem 33

Solve each equation.
$$
-3(x-2)=11
$$

Debasish D.
Debasish D.
Numerade Educator
01:24

Problem 34

Solve each equation.
$$
-5(x-1)=5
$$

Debasish D.
Debasish D.
Numerade Educator
01:49

Problem 35

Solve each equation.
$$
5(2 x+1)=4(3 x-7)
$$

Debasish D.
Debasish D.
Numerade Educator
01:33

Problem 36

Solve each equation.
$$
3(2 x-1)=2(4 x+7)
$$

Debasish D.
Debasish D.
Numerade Educator
01:15

Problem 37

Solve each equation.
$$
5 x-4(x-6)=-11
$$

Debasish D.
Debasish D.
Numerade Educator
01:27

Problem 38

Solve each equation.
$$
3 x-5(2 x+1)=13
$$

Debasish D.
Debasish D.
Numerade Educator
01:26

Problem 39

Solve each equation.
$$
-2(3 x-1)-3=-4
$$

Debasish D.
Debasish D.
Numerade Educator
01:39

Problem 40

Solve each equation.
$$
-6(x-4)-10=-12
$$

Debasish D.
Debasish D.
Numerade Educator
01:56

Problem 41

Solve each equation.
$$
-2(3 x+5)=-3(4 x+3)
$$

Debasish D.
Debasish D.
Numerade Educator
01:54

Problem 42

Solve each equation.
$$
-(2 x-1)=-5(2 x+9)
$$

Debasish D.
Debasish D.
Numerade Educator
01:57

Problem 43

Solve each equation.
$$
3(x-4)-7(x+2)=-2(x+13)
$$

Debasish D.
Debasish D.
Numerade Educator
01:40

Problem 44

Solve each equation.
$$
4(x-2)-3(x-1)=2(x+6)
$$

Debasish D.
Debasish D.
Numerade Educator
01:43

Problem 45

Solve each equation.
$$
-2(3 n-1)+3(n+5)=-4(n-4)
$$

Debasish D.
Debasish D.
Numerade Educator
01:56

Problem 46

Solve each equation.
$$
-3(4 n+2)+2(n-6)=-2(n+1)
$$

Debasish D.
Debasish D.
Numerade Educator
01:57

Problem 47

Solve each equation.
$$
3(2 a-1)-2(5 a+1)=4(3 a+4)
$$

Debasish D.
Debasish D.
Numerade Educator
02:08

Problem 48

Solve each equation.
$$
4(2 a+3)-3(4 a-2)=5(4 a-7)
$$

Debasish D.
Debasish D.
Numerade Educator
02:08

Problem 49

Solve each equation.
$$
-2(n-4)-(3 n-1)=-2+(2 n-1)
$$

Debasish D.
Debasish D.
Numerade Educator
01:55

Problem 50

Solve each equation.
$$
-(2 n-1)+6(n+3)=-4-(7 n-11)
$$

Debasish D.
Debasish D.
Numerade Educator
02:11

Problem 51

Use an algebraic approach to solve each problem. (Objective 2)
If 15 is subtracted from three times a certain number, the result is 27 . Find the number.

Debasish D.
Debasish D.
Numerade Educator

Problem 52

Use an algebraic approach to solve each problem. (Objective 2)
If one is subtracted from seven times a certain number, the result is the same as if 31 is added to three times the number. Find the number.

Check back soon!

Problem 53

Use an algebraic approach to solve each problem. (Objective 2)
Find three consecutive integers whose sum is 42 .

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Problem 54

Use an algebraic approach to solve each problem. (Objective 2)
Find four consecutive integers whose sum is -118 .

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Problem 55

Use an algebraic approach to solve each problem. (Objective 2)
Find three consecutive odd integers such that three times the second minus the third is 11 more than the first.

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Problem 56

Use an algebraic approach to solve each problem. (Objective 2)
Find three consecutive even integers such that four times the first minus the third is six more than twice the second.

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Problem 57

Use an algebraic approach to solve each problem. (Objective 2)
The difference of two numbers is 67 . The larger number is three less than six times the smaller number. Find the numbers.

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Problem 58

Use an algebraic approach to solve each problem. (Objective 2)
The sum of two numbers is 103 . The larger number is one more than five times the smaller number. Find the numbers.

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Problem 59

Use an algebraic approach to solve each problem. (Objective 2)
Angelo is paid double time for each hour he works over 40 hours in a week. Last week he worked 46 hours and earned $$\$ 572$$. What is his normal hourly rate?

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Problem 60

Use an algebraic approach to solve each problem. (Objective 2)
Suppose that a plumbing repair bill, not including tax, was $$\$ 130 .$$ This included $$\$ 25$$ for parts and an amount $_{-}$ for 2 hours of labor. Find the hourly rate that was charged for labor.

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Problem 61

Use an algebraic approach to solve each problem. (Objective 2)
Suppose that Maria has 150 coins consisting of pennies, nickels, and dimes. The number of nickels she has is 10 less than twice the number of pennies; the number of dimes she has is 20 less than three times the number of pennies. How many coins of each kind does she have?

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Problem 62

Use an algebraic approach to solve each problem. (Objective 2)
Hector has a collection of nickels, dimes, and quarters totaling 122 coins. The number of dimes he has is 3 more than four times the number of nickels, and the number of quarters he has is 19 less than the number of dimes. How many coins of each kind does he have?

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Problem 63

Use an algebraic approach to solve each problem. (Objective 2)
The selling price of a ring is $$\$ 750$$. This represents $$\$ 150$$ less than three times the cost of the ring. Find the cost of the ring.

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Problem 64

Use an algebraic approach to solve each problem. (Objective 2)
In a class of 62 students, the number of females is one less than twice the number of males. How many females and how many males are there in the class?

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Problem 65

Use an algebraic approach to solve each problem. (Objective 2)
An apartment complex contains 230 apartments, each having one, two, or three bedrooms. The number of two-bedroom apartments is 10 more than three times the number of three-bedroom apartments. The number of one-bedroom apartments is twice the number of twobedroom apartments. How many apartments of each kind are in the complex?

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Problem 66

Use an algebraic approach to solve each problem. (Objective 2)
Barry sells bicycles on a salary-plus-commission basis. He receives a weekly salary of $$\$ 300$$ and a commission of $$\$ 15$$ for each bicycle that he sells. How many bicycles must he sell in a week to have a total weekly income of $$\$ 750 ?$$

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Problem 67

Explain why the solution set of the equation $x+3=$ $x+4$ is the null set.

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Problem 68

Explain why the solution set of the equation $3(x+5)=$ $3 x+15$ is the entire set of real numbers.

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Problem 69

Barry sells bicycles on a salary-plus-commission basis. He receives a weekly salary of $$\$ 300$$ and a commission of $$\$ 15$$ for each bicycle that he sells. How many bicycles must he sell in a week to have a total weekly income of $$\$ 750 ?$$

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Problem 70

Suppose your friend solved the problem, find two consecutive odd integers whose sum is 28 like this:
$$x+x+1=28$$ $$\begin{aligned} 2 x &=27 \\ x &=\frac{27}{2}=13 \frac{1}{2} \end{aligned}$$
She claims that $13 \frac{1}{2}$ will check in the equation. Where has she gone wrong and how would you help her?

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Problem 71

Make up an equation whose solution set is the null set and explain why this is the solution set.

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Problem 72

Make up an equation whose solution set is the set of all real numbers and explain why this is the solution set.

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Problem 73

Solve each of the following equations.
(a) $5 x+7=5 x-4$
(b) $4(x-1)=4 x-4$
(c) $3(x-4)=2(x-6)$
(d) $7 x-2=-7 x+4$
(e) $2(x-1)+3(x+2)=5(x-7)$
(f) $-4(x-7)=-2(2 x+1)$

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Problem 74

Verify that for any three consecutive integers, the sum of the smallest and largest is equal to twice the middle integer. [Hint: Use $n, n+1,$ and $n+2$ to represent the three consecutive integers.]

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