Question

solve the equation.
3(3 - 3x) = 2(x + 3) - 30
use the sketch tool or paper if it helps with your thinking.

Explanation:

Step1: Expand both sides

First, we expand the left - hand side and the right - hand side of the equation.
For the left - hand side, using the distributive property \(a(b + c)=ab+ac\), we have \(3(3 - 3x)=3\times3-3\times3x = 9-9x\).
For the right - hand side, \(2(x + 3)-30=2\times x+2\times3-30=2x + 6-30=2x-24\).
So the equation becomes \(9-9x=2x - 24\).

Step2: Move the terms with x to one side

We add \(9x\) to both sides of the equation to get rid of the \(-9x\) on the left.
\(9-9x + 9x=2x-24 + 9x\), which simplifies to \(9 = 11x-24\).

Step3: Solve for x

Then we add 24 to both sides of the equation: \(9 + 24=11x-24 + 24\).
\(33 = 11x\).
Next, we divide both sides by 11: \(\frac{33}{11}=\frac{11x}{11}\).
\(x = 3\).

Answer:

\(x = 3\)