Solve 2/3(x −6)=14

Question

(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 \( \boxed{27} \).