To solve the inequality \( \frac{x}{13} < \frac{4}{5} \), we need to isolate \( x \). Here's the step-by-step process:
1. Start with the inequality:
\[
\frac{x}{13} < \frac{4}{5}
\]
2. To eliminate the fraction involving \( x \), multiply both sides of the inequality by 13 (which is the denominator of the fraction on the left side):
\[
13 \cdot \frac{x}{13} < 13 \cdot \frac{4}{5}
\]
3. Simplify the left side:
\[
x < 13 \cdot \frac{4}{5}
\]
4. Calculate the right side:
\[
13 \cdot \frac{4}{5} = \frac{13 \cdot 4}{5} = \frac{52}{5}
\]
Therefore, the solution to the inequality is:
\[
x < \frac{52}{5}
\]
To convert \(\frac{52}{5}\) to a mixed number for easier comparison with the given multiple-choice options:
\[
\frac{52}{5} = 10 \frac{2}{5}
\]
Thus, the correct option is:
C. \( x < 10 \frac{2}{5} \)
Solve x/13 < 4/5.
A. x < 13 4/5
B. x < 4/65
C. x < 10 2/5
D. x > 52/5
1 answer
1 answer