1-7 Solve Equations by Multiplying and Dividing

Ch. 1-7 Solving Equations by Multiplying & Dividing

Steps to solve equation or isolate the variable:

1. Move variable if negative by using the addition property of equality

2. If the number you wish to move is multiplied by the variable use the division property of equality

3. If the number you wish is divided by the variable use the multiplication property of equality

4. Simplify

5. Check to see if your answer is correct

Multiplication Property of

Equality

When you multiply the same number/variable to each side of an equation, the two sides remain equal

5(2) = 105(2) x 3 = 10 x 3

30 = 30

S ÷ 9 = 5S ÷ 9 x 9 = 5 x 9

S = 45-11 = s ÷ 11-11 x 11 = s ÷ 11 x s

-121 = s

Division Property of Equality

When you divide the same number/variable to each side of an equation, the two sides remain equal

5 x 2 = 105 x 2 / 5 = 10 / 5

2 = 2

p x 9 = 36p ÷ 9 x 9 = 36 ÷ 9

p = 4-11 = s x 11-11 ÷ 11 = s ÷ 11 x 11

-1 = s

Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

427 k

742

77 k

61 k

Undo multiplication

4267

Step 1

Step 2

Step 3Check

Simplify

6k

Solving Equations by Dividing

Section 1.8 Solving Equations by Multiplying or Dividing

You want to isolate the

variable

Use Division Property of Equality

The variable

must be positive

Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

n945

99

945 n

n5

5945

n15

Solving Equations by Dividing

Undo multiplication

Step 1

Step 2

Step 3Check

Simplify

Section 1.8 Solving Equations by Multiplying or Dividing

You want to isolate the

variable

Use Division Property of Equality

The variable

must be positive

Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

59

c

959

9 c

45c

5945

451 c

Solving Equations by Multiplying

Undo division

Step 1

Step 2

Step 3Check

Simplify

Section 1.8 Solving Equations by Multiplying or Dividing

You want to isolate the

variable

Use Multiplication Property of Equality

The variable

must be positive

Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

2052 k

501 k

Multiply by the reciprocal

20 5052

Step 1

Step 2

Step 3Check

Simplify50 k

Solving Equations by Multiplying

25

2052

25

k

Section 1.8 Solving Equations by Multiplying or Dividing

You want to isolate the

variable

Use Multiplication Property of Equality

The variable

must be positive

10

Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

59c

Section 1.8 Solving Equations by Multiplying or Dividing

959

9 c

45c

Undo division

5945

Step 1

Step 2

Step 3Check

Simplify

59c

Rewrite

451 c

Solving Equations by Multiplying

You want to isolate the

variable

Use Multiplication Property of Equality

The variable

must be positive

Example 1: Solve each equation by doing the inverse of the operation shown.

a.) -6y = -30 b.) 5x = -15

d.) -12 = 3m e.) 14 = 2m

/-6 /-6

y = 5

/5 /5

x = -3

/2 /2

7 = m Rewrite

m = 7

/3 /3

-4 = m Rewrite

m = -4

Example 2: Solve each equation below by doing the inverse of the operation shown.

a.) b.)

c.) d.)

122

d 24

z

63

2 x 54

1 x

2* *2

d = -24

Divide by 2/3, remember that when you divide by a fraction, you multiply by the reciprocal!

Divide by 1/4, remember that when you divide by a fraction, you multiply by the reciprocal!

-4* * -4

Z = -8

3/2 * * 3/2

x = -9

1

3

4/1 * * 4/1

x = 20

Example 3: Determine whether -5 is a solution to the following equations.

a.) 25v = -5 b.) -2t = 10

c.) d.)9

45 x

735 w

no yes

noyes

Homework

Pg. 40 #12-32 even

SHOW STEPS!!!