Question

Write a rational inequality whose solution set is $\{x\mid -3<x\le 5\}$.

Short answer

The rational inequality is$-\frac{3}{5}<\frac{x}{5}\le 1$.

Step-by-step solution

Given information

The given solution set is $\{x\mid -3<x\le 5\}$.

Determine the rational inequality

Divide by 5 in the given solution set of the inequality.

$$\begin{gathered} -\frac{3}{5}<\frac{x}{5}\le \frac{5}{5} \\ -\frac{3}{5}<\frac{x}{5}\le 1 \end{gathered}$$

Write the conclusion

The inequality is$-\frac{3}{5}<\frac{x}{5}\le 1$.