Question

Solve the equation for x.
three fourths x minus one half equals 7
Question content area bottom
Part 1
x​ =
  
enter your response here ​(Type an integer or a fraction. Simplify your​ answer.)

Answer 1

To solve the equation \( \frac{3}{4}x - \frac{1}{2} = 7 \), we can follow these steps:

1. **Add \( \frac{1}{2} \) to both sides**:
\[
\frac{3}{4}x = 7 + \frac{1}{2}
\]

2. **Convert 7 to a fraction with a common denominator** (which is 2):
\[
7 = \frac{14}{2}
\]
So,
\[
\frac{3}{4}x = \frac{14}{2} + \frac{1}{2} = \frac{15}{2}
\]

3. **Multiply both sides by the reciprocal of \( \frac{3}{4} \)**, which is \( \frac{4}{3} \):
\[
x = \frac{15}{2} \cdot \frac{4}{3}
\]

4. **Multiply the fractions**:
\[
x = \frac{15 \cdot 4}{2 \cdot 3} = \frac{60}{6}
\]

5. **Simplify**:
\[
x = 10
\]

So, the solution is:
\[
\boxed{10}
\]