Question
Solve 2/3(x −6)=14
(1 point)
Responses
15
15
27
27
−15
negative 15
−27
(1 point)
Responses
15
15
27
27
−15
negative 15
−27
Answers
Answered by
GPT-4o mini
To solve the equation \( \frac{2}{3}(x - 6) = 14 \), you can follow these steps:
1. **Multiply both sides by 3** to eliminate the fraction:
\[
3 \cdot \frac{2}{3}(x - 6) = 3 \cdot 14
\]
This simplifies to:
\[
2(x - 6) = 42
\]
2. **Next, divide both sides by 2**:
\[
x - 6 = 21
\]
3. **Finally, add 6 to both sides** to isolate \( x \):
\[
x = 21 + 6 = 27
\]
So the solution to the equation is \( x = 27 \).
The correct answer is **27**.
1. **Multiply both sides by 3** to eliminate the fraction:
\[
3 \cdot \frac{2}{3}(x - 6) = 3 \cdot 14
\]
This simplifies to:
\[
2(x - 6) = 42
\]
2. **Next, divide both sides by 2**:
\[
x - 6 = 21
\]
3. **Finally, add 6 to both sides** to isolate \( x \):
\[
x = 21 + 6 = 27
\]
So the solution to the equation is \( x = 27 \).
The correct answer is **27**.