Let's solve the inequality step-by-step and find the integers that satisfy it:
We start with the compound inequality:
[tex]\[
-4 \leq x + 6 < 5
\][/tex]
First, we need to isolate [tex]\(x\)[/tex] by moving the constant term (6) to the other side of each part of the inequality. We'll do this by subtracting 6 from all parts of the inequality:
[tex]\[
-4 - 6 \leq x + 6 - 6 < 5 - 6
\][/tex]
Simplifying each part, we get:
[tex]\[
-10 \leq x < -1
\][/tex]
This means [tex]\(x\)[/tex] is greater than or equal to -10 and less than -1. Now, we need to find all the integers that satisfy this inequality.
The integers between -10 (including -10) and -1 (not including -1) are:
[tex]\[
-10, -9, -8, -7, -6, -5, -4, -3, -2
\][/tex]
Therefore, the integers that satisfy the inequality [tex]\(-4 \leq x + 6 < 5\)[/tex] are:
[tex]\[
-10, -9, -8, -7, -6, -5, -4, -3, -2
\][/tex]
