Solving Multi-Step Equations

Just remember to follow the steps1. Distribute if you can2. Collect all like terms to simplify3. Isolate the variable using the opposite

order of operations 4. Check your answer

Example # 1

15 – 4 ( y + 3 ) = 1915 - 4y - 12 = 19 3 - 4y =

19 -3 - 3

-4 y = 16-4 -4 y = -4

1st Step: Distribute if you can

2nd Step: Collect like terms to simplify

3rd Step: Isolate the variable using the opposite order of operations

4th step: Check your answer

15 – 4 ( y + 3 ) = 1915 – 4 ( -4 + 3) = 1915 + 16 – 12 = 19 31 – 12 = 19

19 = 19

Example # 2

¼ (12 x – 16) + x = 20

1st Step: Distribute if you can

2nd Step: Collect like terms to simplify

3rd Step: Isolate the variable using the opposite order of operations

4th step: Check your answer

Example # 3

2( 4x + 3) – 5(2x – 1) = 27 1st Step: Distribute if you can

2nd Step: Collect like terms to simplify

3rd Step: Isolate the variable using the opposite order of operations

4th step: Check your answer

The Distributive Property

Our Friend for Solving Equations

Also starring, his Wacky Sidekick, Combining Like Terms

3(2x + 5) = 39

Answer: x = 4

- 4(8 + 5n) = 8

Answer: n = -2

6(3x - 5) - 7x = 25

Answer: x = 5

-2(5 + 6m) + 16 = -90

Answer: m = 8

18x - (8x - 7) = 67

Answer: x = 6

7w - 3(4w + 8) = 11

Answer w = -7

Solving Multi-Step Equations with Distributive Property & Collecting Like

TermsWrite and solve an equation to

find the missing length, a, if the length of the two line segments combined is 36 cm.

2a cm 4a cm

1st Step: Collect like terms to simplify 2nd Step: Isolate the variable using the opposite order of operations

3rd step: Check your answer

Write and solve an equation to find the missing length, a, if the length of the two line segments combined is 36 cm.

2a cm 4a cm

2a + 4a = 36 6a = 36 6 6 a = 6

2(6) + 4(6) = 3612+ 24 36 = 36

1st Step: Distribute if you can2nd Step: Collect like terms to simplify 3rd Step: Isolate the variable using the opposite order of operations 4th step: Check your answer

Six friends go to the movies. Movie tickets are $5 and treats are $2 each. If all 6 friends bought the same number of treats, how many did each person buy if the total spent by all was $54?

6(5 + 2x) = 5430 + 12x = 54-30 -30 12x = 24

12 12 x = 2

6 ( 5 + 2x ) = 546 ( 5 + 2*2) 6 ( 5 + 4) 6(9) 54 = 54