Question

1. $3x - 2 = -2x - 47$ $x = 24$ (with some hand - written calculation steps in the middle)

Explanation:

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

To solve for \(x\), we first eliminate the \(x\) term on the right side. Add \(2x\) to both sides of the equation \(3x - 2=-2x - 47\):
\(3x - 2+2x=-2x - 47+2x\)
Simplifying both sides, we get \(5x - 2=-47\).

Step2: Add \(2\) to both sides

Next, we eliminate the constant term on the left side. 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 both sides by \(5\)

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

Wait, there seems to be an error in the original handwritten solution. Let's re - solve the equation \(3x-2=-2x - 47\) correctly:

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

\(3x-2 + 2x=-2x-47+2x\)
\(5x-2=-47\)

Step2: Add \(2\) to both sides

\(5x-2 + 2=-47+2\)
\(5x=-45\)

Step3: Divide by \(5\)

\(x=\frac{-45}{5}=-9\)

The original handwritten solution has calculation errors. The correct value of \(x\) is \(-9\), not \(24\).

Answer:

The correct solution of the equation \(3x - 2=-2x-47\) is \(x=-9\)