Question

1. solve for x: -10x + 5(x - 5) - 6 = -(2x - 2)

Explanation:

Step1: Expand both sides

First, expand the left - hand side: \(5(x - 5)=5x-25\), so the left - hand side of the equation \(-10x + 5(x - 5)-6\) becomes \(-10x+5x - 25-6=-5x-31\).

Then, expand the right - hand side: \(-(2x - 2)=-2x + 2\).

The equation now is \(-5x-31=-2x + 2\).

Step2: Move the terms with x to one side

Add \(5x\) to both sides of the equation: \(-5x-31 + 5x=-2x + 2+5x\).

Simplifying, we get \(-31 = 3x+2\).

Step3: Solve for x

Subtract 2 from both sides: \(-31-2=3x+2 - 2\).

\(-33 = 3x\).

Divide both sides by 3: \(x=\frac{-33}{3}=-11\).

Answer:

\(x = - 11\)