To solve the inequality [tex]\(-17 < m - 3 \leq 13\)[/tex], we need to break it into two parts and solve each part separately. Here's the step-by-step solution:
1. First part: [tex]\(-17 < m - 3\)[/tex]
To isolate [tex]\(m\)[/tex], we need to add [tex]\(3\)[/tex] to both sides of the inequality:
[tex]\[
-17 + 3 < m - 3 + 3
\][/tex]
This simplifies to:
[tex]\[
-14 < m
\][/tex]
2. Second part: [tex]\(m - 3 \leq 13\)[/tex]
Similarly, to isolate [tex]\(m\)[/tex], we need to add [tex]\(3\)[/tex] to both sides of the inequality:
[tex]\[
m - 3 + 3 \leq 13 + 3
\][/tex]
This simplifies to:
[tex]\[
m \leq 16
\][/tex]
3. Combine the results:
From the first part, we have [tex]\(m > -14\)[/tex]. From the second part, we have [tex]\(m \leq 16\)[/tex]. Combining these two parts, we get the compound inequality:
[tex]\[
-14 < m \leq 16
\][/tex]
So the solution to the inequality [tex]\(-17 < m - 3 \leq 13\)[/tex] is:
[tex]\[
-14 < m \leq 16
\][/tex]
