Question

StartFraction 2 left parenthesis x minus 7 right parenthesis Over 3 EndFraction minus 6 equals 3
​

Answer 1

To solve the equation

\[
\frac{2(x - 7)}{3} - 6 = 3,
\]

let's follow these steps:

1. **Add 6 to both sides** to eliminate the -6:

\[
\frac{2(x - 7)}{3} = 3 + 6
\]

\[
\frac{2(x - 7)}{3} = 9.
\]

2. **Multiply both sides by 3** to eliminate the fraction:

\[
2(x - 7) = 9 \times 3
\]

\[
2(x - 7) = 27.
\]

3. **Divide both sides by 2**:

\[
x - 7 = \frac{27}{2}.
\]

4. **Add 7 to both sides** to solve for \(x\):

\[
x = \frac{27}{2} + 7.
\]

5. **Convert 7 to a fraction** with a common denominator of 2:

\[
7 = \frac{14}{2}.
\]

Thus:

\[
x = \frac{27}{2} + \frac{14}{2} = \frac{27 + 14}{2} = \frac{41}{2}.
\]

Therefore, the solution is:

\[
x = \frac{41}{2}.
\]