Question

1. solve for x.

-12(x - 12) = -9(1 + 7x)

Explanation:

Step1: Expand both sides

First, we expand the left - hand side: \(-12(x - 12)=-12x+144\) (using the distributive property \(a(b - c)=ab - ac\), here \(a=-12\), \(b = x\), \(c = 12\)).
Then, we expand the right - hand side: \(-9(1 + 7x)=-9-63x\) (using the distributive property \(a(b + c)=ab+ac\), here \(a = - 9\), \(b = 1\), \(c = 7x\)).
So the equation becomes \(-12x + 144=-9-63x\).

Step2: Move the x - terms to one side

We add \(63x\) to both sides of the equation to get all the \(x\) - terms on the left.
\(-12x+63x + 144=-9-63x+63x\)
Simplifying the left - hand side: \(51x+144\), and the right - hand side: \(-9\). So the equation is \(51x+144=-9\).

Step3: Isolate the x - term

We subtract 144 from both sides of the equation.
\(51x+144 - 144=-9 - 144\)
Simplifying, we get \(51x=-153\).

Step4: Solve for x

We divide both sides of the equation by 51.
\(x=\frac{-153}{51}\)
Simplifying the fraction, we find that \(x=-3\).

Answer:

\(x = - 3\)