To solve the inequality [tex]\(4x - 12 \leq 16 + 8x\)[/tex], we need to follow these steps:
1. Start by simplifying the inequality:
[tex]\[
4x - 12 \leq 16 + 8x
\][/tex]
2. Isolate the variable term [tex]\(x\)[/tex]. To do this, subtract [tex]\(4x\)[/tex] from both sides of the inequality:
[tex]\[
4x - 12 - 4x \leq 16 + 8x - 4x
\][/tex]
Simplifying this gives:
[tex]\[
-12 \leq 16 + 4x
\][/tex]
3. Isolate the [tex]\(x\)[/tex]-term further by subtracting 16 from both sides:
[tex]\[
-12 - 16 \leq 4x
\][/tex]
Simplifying this gives:
[tex]\[
-28 \leq 4x
\][/tex]
4. Solve for [tex]\(x\)[/tex] by dividing both sides by 4:
[tex]\[
\frac{-28}{4} \leq x
\][/tex]
Simplifying this gives:
[tex]\[
-7 \leq x
\][/tex]
This inequality tells us that [tex]\(x\)[/tex] must be greater than or equal to [tex]\(-7\)[/tex].
Next, we need to check which of the given values [tex]\(-10\)[/tex], [tex]\(-9\)[/tex], [tex]\(-8\)[/tex], or [tex]\(-7\)[/tex] satisfies this inequality.
The values [tex]\(-10\)[/tex], [tex]\(-9\)[/tex], and [tex]\(-8\)[/tex] are all less than [tex]\(-7\)[/tex], so they do not satisfy the inequality. The value [tex]\(-7\)[/tex] is equal to [tex]\(-7\)[/tex] and thus is within the solution set of the inequality.
So, the value of [tex]\(x\)[/tex] that is in the solution set of the inequality [tex]\(4x - 12 \leq 16 + 8x\)[/tex] is:
[tex]\[
\boxed{-7}
\][/tex]
