Question

introduction to compound inequalities
for one photography session, dexter earns no less than $50, but no more than $100. which inequality can be used to represent his earnings, $e$?
$e \geq 50$ or $e \leq 100$
$e > 50$ or $e < 100$
$50 < e < 100$
$50 \leq e \leq 100$

Explanation:

Step1: Interpret "no less than $50"

This means earnings $e$ is greater than or equal to 50, so $e \geq 50$.

Step2: Interpret "no more than $100"

This means earnings $e$ is less than or equal to 100, so $e \leq 100$.

Step3: Combine the inequalities

Combine the two conditions into a single compound inequality.

Answer:

$50 \leq e \leq 100$ (matches the fourth option: 50 ≤ e ≤ 100)