Solving Multi-Step Equations Just remember to follow the steps 1. Distribute if you can 2. Collect all like terms to simplify 3. Isolate the variable using the opposite order of operations 4. Check your answer
Example # 1 1 st Step: Distribute if you can 15 – 4 ( y + 3 ) = 19 15 - 4 y - 12 = 19 3 - 4 y = 19 -3 -3 -4 y = 16 -4 -4 y = -4 2 nd Step: Collect like terms to simplify 3 rd Step: Isolate the variable using the opposite order of operations 4 th step: Check your answer 15 – 4 ( y + 3 ) = 19 15 – 4 ( -4 + 3) = 19 15 + 16 – 12 = 19 31 – 12 = 19 19 = 19
Example # 2 ¼ (12 x – 16) + x = 1 st Step: Distribute if you can 20 2 nd Step: Collect like terms to simplify 3 rd Step: Isolate the variable using the opposite order of operations 4 th step: Check your answer
Example # 3 2( 4 x + 3) – 5(2 x – 1) = 27 1 st Step: Distribute if you can 2 nd Step: Collect like terms to simplify 3 rd Step: Isolate the variable usin the opposite order of operations 4 th step: Check your answer
The Distributive Property Our Friend for Solving Equations Also starring, his Wacky Sidekick, Combining Like Terms
3(2 x + 5) = 39
Answer: x = 4
- 4(8 + 5 n) = 8
Answer: n = -2
6(3 x - 5) - 7 x = 25
Answer: x = 5
-2(5 + 6 m) + 16 = -90
Answer: m = 8
18 x - (8 x - 7) = 67
Answer: x = 6
7 w - 3(4 w + 8) = 11
Answer w = -7
Solving Multi-Step Equations with Distributive Property & Collecting Like Terms Write and solve an equation to find the missing length, a, if the length of the two line segments combined is 36 cm. 2 a cm 4 a cm
Write and solve an equation to find the missing length, a, if the length of the two line segments combined is 36 cm. 2 a cm 4 a cm 1 st Step: Collect like terms to simplify 2 a + 4 a = 36 6 6 a = 6 2 nd Step: Isolate the variable using the opposite order of operations 3 rd step: Check your answer 2(6) + 4(6) = 36 12+ 24 36 = 36
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 + 2 x) = 54 30 + 12 x = 54 -30 12 x = 24 12 12 x = 2 1 st Step: Distribute if you can 2 nd Step: Collect like terms to simplify 3 rd Step: Isolate the variable using the opposite order of operations 4 th step: Check your answer 6 ( 5 + 2 x ) = 54 6 ( 5 + 2*2) 6 ( 5 + 4) 6(9) 54 = 54
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