Question

solve for x:
-2(8x + 1) - 1 = -7(2x - 3) - x

Explanation:

Step1: Distribute the -2 and -7

We first apply the distributive property to both sides of the equation. For the left side, we have \(-2(8x + 1)\), which becomes \(-16x - 2\). Then we subtract 1, so the left side is \(-16x - 2 - 1 = -16x - 3\). For the right side, we have \(-7(2x - 3)\), which becomes \(-14x + 21\). Then we subtract \(x\), so the right side is \(-14x + 21 - x = -15x + 21\). So now our equation is:
\[
-16x - 3 = -15x + 21
\]

Step2: Add 16x to both sides

To get all the \(x\) terms on one side, we add \(16x\) to both sides of the equation. This gives us:
\[
-3 = x + 21
\]

Step3: Subtract 21 from both sides

Now we solve for \(x\) by subtracting 21 from both sides:
\[
x = -3 - 21 = -24
\]

Answer:

\(x = -24\)