Question

Caitlyn needs to solve the equation: 2(3x+1)=3(2-x).

She solves for x in 5 steps:
6x+2 = 6 - 3x
2 = 6 - 9x
-4 = -9x
4/9 = x
x = 4/9

What is the justification for each of the steps that Caitlyn took? Give the Algebraic Property for each step.

Answer 1

Step 1:Simplify both sides of the equation.2(3x+1)=3(2−x)(2)(3x)+(2)(1)=(3)(2)+(3)(−x)(Distribute)6x+2=6+−3x6x+2=−3x+6
Step 2: Add 3x to both sides.6x+2+3x=−3x+6+3x9x+2=6
Step 3:Subtract 2 from both sides.9x+2−2=6−29x=4
Step 4:Divide both sides by 9.9x9=49

hope it helps :)