2/3 ( x -4 ) = -6

Answer 1

To solve the equation \( \frac{2}{3} ( x - 4 ) = -6 \), follow these steps:

1. Eliminate the fraction by multiplying both sides of the equation by 3: \[ 3 \cdot \frac{2}{3} ( x - 4 ) = 3 \cdot (-6) \] This simplifies to: \[ 2 ( x - 4 ) = -18 \]

2. Distribute the 2 on the left side: \[ 2x - 8 = -18 \]

3. Add 8 to both sides to isolate the term with \( x \): \[ 2x = -18 + 8 \] Simplifying the right side gives: \[ 2x = -10 \]

4. Divide both sides by 2 to solve for \( x \): \[ x = \frac{-10}{2} = -5 \]

Thus, the solution is \[ \boxed{-5} \]