Question

1. \\( 3x - 2 = -2x - 47 \\)

Explanation:

Step1: Add \(2x\) to both sides

To get all \(x\)-terms on one side, we add \(2x\) to both sides of the equation \(3x - 2=-2x - 47\).
\(3x - 2+2x=-2x - 47+2x\)
Simplifying both sides, we have \(5x - 2=-47\).

Step2: Add 2 to both sides

To isolate the term with \(x\), we add 2 to both sides of the equation \(5x - 2=-47\).
\(5x - 2 + 2=-47+2\)
Simplifying both sides, we get \(5x=-45\).

Step3: Divide by 5

To solve for \(x\), we divide both sides of the equation \(5x=-45\) by 5.
\(\frac{5x}{5}=\frac{-45}{5}\)
Simplifying, we find \(x = - 9\).

Answer:

\(x=-9\)