Question

Solve x/13<4/5
.(1 point)
Responses

x<465
x less than Start Fraction 4 over 65 End Fraction

x<1345
x less than 13 Start Fraction 4 over 5 End Fraction

x<1025
x less than 10 Start Fraction 2 over 5 End Fraction

x>525

Answer 1

To solve the inequality \( \frac{x}{13} < \frac{4}{5} \), we need to isolate \( x \).

1. Start by multiplying both sides of the inequality by 13 (since 13 is positive, the direction of the inequality does not change):

\[
x < 13 \cdot \frac{4}{5}
\]

2. Calculate the right side:

\[
13 \cdot \frac{4}{5} = \frac{52}{5}
\]

3. To convert \( \frac{52}{5} \) to a decimal, divide 52 by 5:

\[
\frac{52}{5} = 10.4
\]

Therefore, the solution to the inequality is:

\[
x < \frac{52}{5} \quad \text{or} \quad x < 10.4
\]

Now, let's convert \( \frac{52}{5} \) into a more suitable form if necessary. The numerical value is equivalent to:

\[
x < 10\frac{2}{5}
\]

The answer options given do not match directly with our result. Thus, there seems to be a focus on interpreting \( \frac{52}{5} \) correctly in the response options.

From the response options provided, none are exact. However, the closest correct interpretation is:

**x < 13 \( \frac{4}{5} \)** (since \( 13 \times \frac{4}{5} = \frac{52}{5} = 10.4 \))

So, the most suitable response from the options listed would be:

**x < 13 \( \frac{4}{5} \)**.