Answer :

Let's solve the compound inequality step-by-step:

The inequality given is:
[tex]\[ -16 \leq x - 11 < -7 \][/tex]

This compound inequality can be broken into two separate inequalities:
1. [tex]\(-16 \leq x - 11\)[/tex]
2. [tex]\(x - 11 < -7\)[/tex]

Let's solve each one separately:

1. Solve [tex]\(-16 \leq x - 11\)[/tex]:

- Add 11 to both sides to isolate [tex]\(x\)[/tex]:
[tex]\[
-16 + 11 \leq x
\][/tex]
[tex]\[
-5 \leq x
\][/tex]

So, [tex]\(x \geq -5\)[/tex].

2. Solve [tex]\(x - 11 < -7\)[/tex]:

- Add 11 to both sides to isolate [tex]\(x\)[/tex]:
[tex]\[
x - 11 + 11 < -7 + 11
\][/tex]
[tex]\[
x < 4
\][/tex]

Now, combine the solutions from both inequalities:

From the first inequality, we have [tex]\(x \geq -5\)[/tex], and from the second inequality, we have [tex]\(x < 4\)[/tex].

Therefore, the solution to the compound inequality [tex]\(-16 \leq x - 11 < -7\)[/tex] is:
[tex]\[
-5 \leq x < 4
\][/tex]

This means that [tex]\(x\)[/tex] can be any number greater than or equal to [tex]\(-5\)[/tex] and less than 4.

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