To solve the equation \( \frac{7}{8}(r - \frac{5}{21}) = \frac{3}{2} \), follow these steps:
-
Isolate the term with \( r \):
- Start by eliminating the fraction on the left side. Multiply both sides of the equation by \( \frac{8}{7} \): \[ r - \frac{5}{21} = \frac{3}{2} \cdot \frac{8}{7} \]
-
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: \[ r - \frac{5}{21} = \frac{12}{7} \]
-
Add \( \frac{5}{21} \) to both sides: \[ r = \frac{12}{7} + \frac{5}{21} \]
-
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: \[ r = \frac{41}{21} \]