Sure, let's solve the inequality step by step. We are given:
[tex]\[
-4 \leq x + 6 < 5
\][/tex]
First, we need to isolate [tex]\( x \)[/tex] in the inequality. To do this, we will subtract 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]
Now, we need to find all the integers that satisfy this inequality [tex]\( -10 \leq x < -1 \)[/tex]. This includes all integers starting from [tex]\(-10\)[/tex] up to [tex]\(-2\)[/tex] (since [tex]\(-1\)[/tex] is not included as it's a strict inequality).
List of integers within the specified range:
[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]
