To solve the inequality \( x \cdot 0.13 < \frac{4}{5} \), first, you can convert \( 0.13 \) into a fraction for easier manipulation.
We know that: \[ 0.13 = \frac{13}{100} \]
Thus, we rewrite the inequality as: \[ x \cdot \frac{13}{100} < \frac{4}{5} \]
Next, we can eliminate the fraction by multiplying both sides by \( 100 \) (note that 100 is positive, so the inequality direction does not change): \[ x \cdot 13 < \frac{4}{5} \cdot 100 \]
Calculating the right-hand side: \[ \frac{4}{5} \cdot 100 = 80 \]
Now we have: \[ 13x < 80 \]
To isolate \( x \), divide both sides by \( 13 \): \[ x < \frac{80}{13} \]
Calculating \( \frac{80}{13} \): \[ \frac{80}{13} \approx 6.1538 \quad (\text{to four decimal places}) \]
Thus, the solution is: \[ x < \frac{80}{13} \quad \text{or} \quad x < 6.1538 \]
Hence, the final answer is: \[ x < \frac{80}{13} \]