Question

To solve the equation, Lorie applies the distributive property, combines like terms, then applies the addition and subtraction properties of equality to isolate the variable term on one side of the equation and the constant term on the other side. What are the possible coefficients of x after Lorie has completed these steps?

10 (one-half x + 2) minus 5 = 3 (x minus 6) + 1
–32 and 2
–2 and 32
–2 and 2
–32 and 32

Answer 1

Start by distributing and combining like terms:

10(1/2 x + 2) − 5 = 3(x − 6) + 1
5x + 20 − 5 = 3x − 18 + 1
5x + 15 = 3x − 17

Isolating the variable can be done two ways:

- Move 3x to the left: 5x − 3x + 15 = −17 → 2x + 15 = −17 → 2x = −32 (coefficient 2)
- Or move 5x to the right: 15 = 3x − 5x − 17 → 15 = −2x − 17 → 32 = −2x (coefficient −2)

So the possible coefficients are −2 and 2.