Question

When solving the equation 4(3x+2)-9=8x+7, Emily wrote 4 (3x+2)=8x+16 as her first step. which property justifies Emily first step?

1)commutative property of addition
2)addition property of equality
3)multiplication property of equality
4)distributive property of multiplication over addition

Answer 1

4(3x + 2) - 9 = 8x + 7
4(3x) + 4(2) - 9 = 8x + 7
12x + 8 - 9 = 8x + 7
12x - 1 = 8x + 7
- 8x - 8x
4x - 1 = 7
+ 1 + 1
4x = 8
4 4
x = 2

The property that justifies Emily's first step is the addition property of equality (2).