Match the statement with the most appropriate choice from the column on the right.

The equations $x+3=7$ and $6 x=24$

a) Coefficient

b) Equivalent expressions

c) Equivalent equations

d) The multiplication principle

e) The addition principle

f) Solution

Sheila A.

Numerade Educator

Match the statement with the most appropriate choice from the column on the right.

The expressions $3(x-2)$ and $3 x-6$

a) Coefficient

b) Equivalent expressions

c) Equivalent equations

d) The multiplication principle

e) The addition principle

f) Solution

Joshua F.

Numerade Educator

Match the statement with the most appropriate choice from the column on the right.

A replacement that makes an equation true

a) Coefficient

b) Equivalent expressions

c) Equivalent equations

d) The multiplication principle

e) The addition principle

f) Solution

Sheila A.

Numerade Educator

Match the statement with the most appropriate choice from the column on the right.

The role of 9 in $9 a b$

a) Coefficient

b) Equivalent expressions

c) Equivalent equations

d) The multiplication principle

e) The addition principle

f) Solution

Joshua F.

Numerade Educator

Match the statement with the most appropriate choice from the column on the right.

The principle used to solve $\frac{2}{3} \cdot x=-4 \quad$

a) Coefficient

b) Equivalent expressions

c) Equivalent equations

d) The multiplication principle

e) The addition principle

f) Solution

Sheila A.

Numerade Educator

Match the statement with the most appropriate choice from the column on the right.

The principle used to solve $\frac{2}{3}+x=-4 \quad$

a) Coefficient

b) Equivalent expressions

c) Equivalent equations

d) The multiplication principle

e) The addition principle

f) Solution

Joshua F.

Numerade Educator

Match the equation with the step, from the column on the right, that would be used to solve the equation.

$6 x=30$

a) Add 6 to both sides.

b) Subtract 6 from both sides.

c) Multiply both sides by $6 .$

d) Divide both sides by 6

Sheila A.

Numerade Educator

Match the equation with the step, from the column on the right, that would be used to solve the equation.

$x+6=30 \quad$

a) Add 6 to both sides.

b) Subtract 6 from both sides.

c) Multiply both sides by $6 .$

d) Divide both sides by 6

Joshua F.

Numerade Educator

Match the equation with the step, from the column on the right, that would be used to solve the equation.

$\frac{1}{6} x=30 \quad$

a) Add 6 to both sides.

b) Subtract 6 from both sides.

c) Multiply both sides by $6 .$

d) Divide both sides by 6

Sheila A.

Numerade Educator

Match the equation with the step, from the column on the right, that would be used to solve the equation.

$x-6=30 \quad$

a) Add 6 to both sides.

b) Subtract 6 from both sides.

c) Multiply both sides by $6 .$

d) Divide both sides by 6

Joshua F.

Numerade Educator

The Try Exercises for examples are indicated by a shaded block on the exercise number. Answers to these exercises appear at the end of the exercise set as well as at the back of the book.

Determine whether the given number is a solution of the given equation.

$$

6-x=-2 ; 4

$$

Sheila A.

Numerade Educator

The Try Exercises for examples are indicated by a shaded block on the exercise number. Answers to these exercises appear at the end of the exercise set as well as at the back of the book.

Determine whether the given number is a solution of the given equation.

$$

6-x=-2 ; 8

$$

Joshua F.

Numerade Educator

The Try Exercises for examples are indicated by a shaded block on the exercise number. Answers to these exercises appear at the end of the exercise set as well as at the back of the book.

Determine whether the given number is a solution of the given equation.

$$

\frac{2}{3} t=12 ; 18

$$

Sheila A.

Numerade Educator

Determine whether the given number is a solution of the given equation.

$$

\frac{2}{3} t=12 ; 8

$$

Joshua F.

Numerade Educator

Determine whether the given number is a solution of the given equation.

$$

x+7=3-x ;-2

$$

Sheila A.

Numerade Educator

Determine whether the given number is a solution of the given equation.

$$

-4+x=5 x ;-1

$$

Joshua F.

Numerade Educator

Determine whether the given number is a solution of the given equation.

$$

4-\frac{1}{5} n=8 ;-20

$$

Sheila A.

Numerade Educator

Determine whether the given number is a solution of the given equation.

$$

-3=5-\frac{n}{2} ; 4

$$

Joshua F.

Numerade Educator

Solve using the addition principle. Don't forget to check!

$$

x+5=8

$$

Joshua F.

Numerade Educator

Solve using the addition principle. Don't forget to check!

$$

y+7=-4

$$

Sheila A.

Numerade Educator

Solve using the addition principle. Don't forget to check!

$$

t+6=43

$$

Joshua F.

Numerade Educator

Solve using the addition principle. Don't forget to check!

$$

-6=y+25

$$

Sheila A.

Numerade Educator

Solve using the addition principle. Don't forget to check!

$$

-5=x+8

$$

Joshua F.

Numerade Educator

Solve using the addition principle. Don't forget to check!

$$

x-8=5

$$

Sheila A.

Numerade Educator

Solve using the addition principle. Don't forget to check!

$$

x-9=6

$$

Joshua F.

Numerade Educator

Solve using the addition principle. Don't forget to check!

$$

12=-7+y

$$

Sheila A.

Numerade Educator

Solve using the addition principle. Don't forget to check!

$$

15=-8+z

$$

Joshua F.

Numerade Educator

Solve using the addition principle. Don't forget to check!

$$

-5+t=-9

$$

Sheila A.

Numerade Educator

Solve using the addition principle. Don't forget to check!

$$

-6+y=-21

$$

Joshua F.

Numerade Educator

Solve using the addition principle. Don't forget to check!

$$

r+\frac{1}{3}=\frac{8}{3}

$$

Sheila A.

Numerade Educator

Solve using the addition principle. Don't forget to check!

$$

t+\frac{3}{8}=\frac{5}{8}

$$

Joshua F.

Numerade Educator

Solve using the addition principle. Don't forget to check!

$$

x-\frac{3}{5}=-\frac{7}{10}

$$

Sheila A.

Numerade Educator

Solve using the addition principle. Don't forget to check!

$$

x-\frac{2}{3}=-\frac{5}{6}

$$

Joshua F.

Numerade Educator

Solve using the addition principle. Don't forget to check!

$$

-\frac{1}{5}+z=-\frac{1}{4}

$$

Sheila A.

Numerade Educator

Solve using the addition principle. Don't forget to check!

$$

-\frac{1}{8}+y=-\frac{3}{4}

$$

Joshua F.

Numerade Educator

Solve using the addition principle. Don't forget to check!

$$

m+3.9=5.4

$$

Sheila A.

Numerade Educator

Solve using the addition principle. Don't forget to check!

$$

y+5.3=8.7

$$

Joshua F.

Numerade Educator

Solve using the addition principle. Don't forget to check!

$$

-9.7=-4.7+y

$$

Sheila A.

Numerade Educator

Solve using the addition principle. Don't forget to check!

$$

-7.8=2.8+x

$$

Joshua F.

Numerade Educator

Solve using the multiplication principle. Don't forget to check!

$$

5 x=70

$$

Sheila A.

Numerade Educator

Solve using the multiplication principle. Don't forget to check!

$$

3 x=39

$$

Joshua F.

Numerade Educator

Solve using the multiplication principle. Don't forget to check!

$$

84=7 n

$$

Sheila A.

Numerade Educator

Solve using the multiplication principle. Don't forget to check!

$$

56=7 t

$$

Joshua F.

Numerade Educator

Solve using the multiplication principle. Don't forget to check!

$$

-x=23

$$

Sheila A.

Numerade Educator

Solve using the multiplication principle. Don't forget to check!

$$

100=-x

$$

Joshua F.

Numerade Educator

Solve using the multiplication principle. Don't forget to check!

$$

-t=-8

$$

Sheila A.

Numerade Educator

Solve using the multiplication principle. Don't forget to check!

$$

-68=-r

$$

Joshua F.

Numerade Educator

Solve using the multiplication principle. Don't forget to check!

$$

2 x=-5

$$

Sheila A.

Numerade Educator

Solve using the multiplication principle. Don't forget to check!

$$

-3 x=5

$$

Joshua F.

Numerade Educator

Solve using the multiplication principle. Don't forget to check!

$$

-1.3 a=-10.4

$$

Sheila A.

Numerade Educator

Solve using the multiplication principle. Don't forget to check!

$$

-3.4 t=-20.4

$$

Joshua F.

Numerade Educator

Solve using the multiplication principle. Don't forget to check!

$$

\frac{y}{-8}=11

$$

Sheila A.

Numerade Educator

Solve using the multiplication principle. Don't forget to check!

$$

\frac{a}{4}=13

$$

Joshua F.

Numerade Educator

Solve using the multiplication principle. Don't forget to check!

$$

\frac{4}{5} x=16

$$

Sheila A.

Numerade Educator

Solve using the multiplication principle. Don't forget to check!

$$

\frac{3}{4} x=27

$$

Joshua F.

Numerade Educator

Solve using the multiplication principle. Don't forget to check!

$$

\frac{-x}{6}=9

$$

Sheila A.

Numerade Educator

Solve using the multiplication principle. Don't forget to check!

$$

\frac{-t}{5}=9

$$

Joshua F.

Numerade Educator

Solve using the multiplication principle. Don't forget to check!

$$

\frac{1}{9}=\frac{z}{5}

$$

Sheila A.

Numerade Educator

Solve using the multiplication principle. Don't forget to check!

$$

\frac{2}{7}=\frac{x}{3}

$$

Joshua F.

Numerade Educator

Solve using the multiplication principle. Don't forget to check!

$$

-\frac{3}{5} r=-\frac{3}{5}

$$

Sheila A.

Numerade Educator

Solve using the multiplication principle. Don't forget to check!

$$

-\frac{2}{5} y=-\frac{4}{15}

$$

Joshua F.

Numerade Educator

Solve using the multiplication principle. Don't forget to check!

$$

\frac{-3 r}{2}=-\frac{27}{4}

$$

Sheila A.

Numerade Educator

Solve using the multiplication principle. Don't forget to check!

$$

\frac{5 x}{7}=-\frac{10}{14}

$$

Joshua F.

Numerade Educator

Solve. The symbol indicates an exercise designed to give practice using a calculator.

$$

4.5+t=-3.1

$$

Sheila A.

Numerade Educator

Solve. The symbol indicates an exercise designed to give practice using a calculator.

$$

\frac{3}{4} x=18

$$

Joshua F.

Numerade Educator

$$

\frac{3}{4} x=18

$$

Sheila A.

Numerade Educator

Solve. The symbol indicates an exercise designed to give practice using a calculator.

$$

t-7.4=-12.9

$$

Joshua F.

Numerade Educator

Solve. The symbol indicates an exercise designed to give practice using a calculator.

$$

x-4=-19

$$

Sheila A.

Numerade Educator

Solve. The symbol indicates an exercise designed to give practice using a calculator.

$$

y-6=-14

$$

Joshua F.

Numerade Educator

Solve. The symbol indicates an exercise designed to give practice using a calculator.

$$

-12 x=72

$$

Sheila A.

Numerade Educator

Solve. The symbol indicates an exercise designed to give practice using a calculator.

$$

-15 x=105

$$

Joshua F.

Numerade Educator

Solve. The symbol indicates an exercise designed to give practice using a calculator.

$$

48=-\frac{3}{8} y

$$

Sheila A.

Numerade Educator

Solve. The symbol indicates an exercise designed to give practice using a calculator.

$$

14=t+27

$$

Joshua F.

Numerade Educator

Solve. The symbol indicates an exercise designed to give practice using a calculator.

$$

a-\frac{1}{6}=-\frac{2}{3}

$$

Sheila A.

Numerade Educator

Solve. The symbol indicates an exercise designed to give practice using a calculator.

$$

-\frac{x}{7}=\frac{2}{9}

$$

Joshua F.

Numerade Educator

Solve. The symbol indicates an exercise designed to give practice using a calculator.

$$

-24=\frac{8 x}{5}

$$

Sheila A.

Numerade Educator

Solve. The symbol indicates an exercise designed to give practice using a calculator.

$$

\frac{1}{5}+y=-\frac{3}{10}

$$

Joshua F.

Numerade Educator

Solve. The symbol indicates an exercise designed to give practice using a calculator.

$$

-\frac{4}{3} t=-16

$$

Sheila A.

Numerade Educator

Solve. The symbol indicates an exercise designed to give practice using a calculator.

$$

\frac{17}{35}=-x

$$

Joshua F.

Numerade Educator

Solve. The symbol indicates an exercise designed to give practice using a calculator.

$$

-483.297=-794.053+t

$$

Sheila A.

Numerade Educator

Solve. The symbol indicates an exercise designed to give practice using a calculator.

$$

-0.2344 x=2028.732

$$

Joshua F.

Numerade Educator

When solving an equation, how do you determine what number to add, subtract, multiply, or divide by on both sides of that equation?

Sheila A.

Numerade Educator

What is the difference between equivalent expressions and equivalent equations?

Joshua F.

Numerade Educator

To prepare for Section $2.2,$ review the rules for order of operations (Section $1.8)$

Simplify. [ 1.8]

$$

3 \cdot 4-18

$$

Sheila A.

Numerade Educator

To prepare for Section $2.2,$ review the rules for order of operations (Section $1.8)$

Simplify. [ 1.8]

$$

14-2(7-1)

$$

Joshua F.

Numerade Educator

To prepare for Section $2.2,$ review the rules for order of operations (Section $1.8)$

Simplify. [ 1.8]

$$

16 \div(2-3 \cdot 2)+5

$$

Sheila A.

Numerade Educator

To prepare for Section $2.2,$ review the rules for order of operations (Section $1.8)$

Simplify. [ 1.8]

$$

12-5 \cdot 2^{3}+4 \cdot 3

$$

Joshua F.

Numerade Educator

To solve $-3.5=14 t,$ Gregory adds 3.5 to both sides. Will this form an equivalent equation? Will it help solve the equation? Explain.

Sheila A.

Numerade Educator

Explain why it is not necessary to state a subtraction principle: For any real numbers $a, b,$ and $c, a=b$ is equivalent to $a-c=b-c$

Joshua F.

Numerade Educator

Solve for $x .$ Assume $a, c, m \neq 0$

$$

c \cdot \frac{21}{a}=\frac{7 c x}{2 a}

$$

Joshua F.

Numerade Educator

Solve for $x .$ Assume $a, c, m \neq 0$

$$

\text { If } t-3590=1820, \text { find } t+3590

$$

Sheila A.

Numerade Educator

Solve for $x .$ Assume $a, c, m \neq 0$

$$

\text { If } n+268=124, \text { find } n-268

$$

Joshua F.

Numerade Educator

Alayna makes a calculation and gets an answer of $22.5 .$ On the last step, she multiplies by 0.3 when she should have divided by 0.3. What is the correct answer?

Sheila A.

Numerade Educator

Are the equations $x=5$ and $x^{2}=25$ equivalent? Why or why not?

Joshua F.

Numerade Educator