Question

Solve for r in the equation 7/8(r−5/21)=3/2 .(1 point)

Answer 1

To solve the equation \( \frac{7}{8}(r - \frac{5}{21}) = \frac{3}{2} \), follow these steps:

1. **Isolate the term with \( r \)**:
- Start by eliminating the fraction on the left side. Multiply both sides of the equation by \( \frac{8}{7} \):
\[
r - \frac{5}{21} = \frac{3}{2} \cdot \frac{8}{7}
\]

2. **Calculate \( \frac{3}{2} \cdot \frac{8}{7} \)**:
\[
\frac{3 \cdot 8}{2 \cdot 7} = \frac{24}{14} = \frac{12}{7}
\]
The equation now becomes:
\[
r - \frac{5}{21} = \frac{12}{7}
\]

3. **Add \( \frac{5}{21} \) to both sides**:
\[
r = \frac{12}{7} + \frac{5}{21}
\]

4. **Find a common denominator to add the fractions**:
- The least common multiple of \( 7 \) and \( 21 \) is \( 21 \).
- Convert \( \frac{12}{7} \) to have a denominator of \( 21 \):
\[
\frac{12}{7} = \frac{12 \cdot 3}{7 \cdot 3} = \frac{36}{21}
\]
Now, we can add the fractions:
\[
r = \frac{36}{21} + \frac{5}{21} = \frac{36 + 5}{21} = \frac{41}{21}
\]

Thus, the solution is:
\[
r = \frac{41}{21}
\]