Question

Solve 2/3(x −6)=14
(1 point)
Responses

27
27

−27
negative 27

15
15

−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 \(x\):

\[
2x - 12 + 12 = 42 + 12
\]

This simplifies to:

\[
2x = 54
\]

4. **Divide by 2** to solve for \(x\):

\[
x = \frac{54}{2}
\]

This simplifies to:

\[
x = 27
\]

So, the solution is \( \boxed{27} \).