Question

1. solve for m.

17 ≤ 11 - m

Explanation:

Step1: Subtract 11 from both sides

To isolate the term with \( m \), we first subtract 11 from both sides of the inequality \( 17 \leq 11 - m \).
\[
17 - 11 \leq 11 - m - 11
\]
Simplifying both sides gives:
\[
6 \leq -m
\]

Step2: Multiply both sides by -1 (and reverse inequality)

When we multiply or divide an inequality by a negative number, we must reverse the inequality sign. So we multiply both sides of \( 6 \leq -m \) by -1.
\[
6 \times (-1) \geq -m \times (-1)
\]
Simplifying both sides gives:
\[
-6 \geq m
\]
Which can also be written as \( m \leq -6 \).

Answer:

\( m \leq -6 \)