Question

1. the steps at the right show cam’s work in solving an equation. circle the line where he makes a mistake. then, find the correct solution to the equation.

-12x + 12 = -3(5x + 8)
-12x + 12 = -15x + 24
3x + 12 = 24
3x = 12
x = 4

Explanation:

Step1: Expand the right side of the equation

When expanding \(-3(5x + 8)\) using the distributive property \(a(b + c)=ab+ac\) (here \(a=-3\), \(b = 5x\), \(c = 8\)), we should get \(-3\times5x+(-3)\times8=-15x-24\), not \(-15x + 24\). So the line \(-12x + 12=-15x + 24\) is wrong.

Step2: Correctly solve the equation

Start with the correct expansion: \(-12x+12=-15x - 24\).
Add \(15x\) to both sides: \(-12x+15x + 12=-15x+15x - 24\), which simplifies to \(3x+12=-24\).
Subtract \(12\) from both sides: \(3x+12 - 12=-24 - 12\), so \(3x=-36\).
Divide both sides by \(3\): \(x=\frac{-36}{3}\).

Answer:

The line \(-12x + 12=-15x + 24\) is wrong. The correct solution is \(x=-12\).