Question

Solve 2/3(x −6)=14(1 point)
Responses

27
27

−27
negative 27

−15
negative 15

15

Answer 1

Let's solve the equation step by step:

Given equation:
\[
\frac{2}{3}(x - 6) = 14
\]

1. First, we can 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. Next, distribute the 2 on the left side:
\[
2x - 12 = 42
\]

3. Now, add 12 to both sides to isolate the term with \(x\):
\[
2x = 42 + 12
\]
\[
2x = 54
\]

4. Finally, divide both sides by 2 to solve for \(x\):
\[
x = \frac{54}{2} = 27
\]

The solution is:
\[
\boxed{27}
\]