Question

solve for m.
-5 > -2m - 1 ≥ -11
write your answer as a compound inequality with integers.

Explanation:

Step1: Add 1 to all parts

To isolate the term with \( m \), we add 1 to each part of the compound inequality.
\( -5 + 1 > -2m - 1 + 1 \geq -11 + 1 \)
Simplifying each part: \( -4 > -2m \geq -10 \)

Step2: Divide all parts by -2 (reverse inequalities)

When dividing by a negative number, the direction of the inequality signs reverses.
\( \frac{-4}{-2} < \frac{-2m}{-2} \leq \frac{-10}{-2} \)
Simplifying each part: \( 2 < m \leq 5 \)

Answer:

\( 2 < m \leq 5 \)