Solve 2/3 (x − 6 ) = 14

Question

(1 point)
Responses

−15
negative 15

−27
negative 27

27
27

15

Answer 1

To solve the equation \( \frac{2}{3}(x - 6) = 14 \), follow these steps:

1. Eliminate the fraction by multiplying both sides of the equation by 3: \[ 3 \cdot \frac{2}{3}(x - 6) = 3 \cdot 14 \] This simplifies to: \[ 2(x - 6) = 42 \]

2. Distribute the 2 on the left side: \[ 2x - 12 = 42 \]

3. Add 12 to both sides to isolate the term with x: \[ 2x = 42 + 12 \] This simplifies to: \[ 2x = 54 \]

4. Divide both sides by 2: \[ x = \frac{54}{2} \] This simplifies to: \[ x = 27 \]

Thus, the solution to the equation is \( x = 27 \).

The correct response is 27.