To solve the inequality [tex]\(4x - 12 \leq 16 + 8x\)[/tex], we need to isolate [tex]\(x\)[/tex] on one side of the inequality.
1. Start by subtracting [tex]\(4x\)[/tex] from both sides:
[tex]\[
4x - 12 - 4x \leq 16 + 8x - 4x
\][/tex]
This simplifies to:
[tex]\[
-12 \leq 16 + 4x
\][/tex]
2. Next, subtract 16 from both sides to further isolate [tex]\(x\)[/tex]:
[tex]\[
-12 - 16 \leq 4x
\][/tex]
Simplifying this gives:
[tex]\[
-28 \leq 4x
\][/tex]
3. Now, divide both sides by 4 to solve for [tex]\(x\)[/tex]:
[tex]\[
\frac{-28}{4} \leq x
\][/tex]
This simplifies to:
[tex]\[
-7 \leq x \quad \text{or} \quad x \geq -7
\][/tex]
This means the solution to the inequality [tex]\(4x - 12 \leq 16 + 8x\)[/tex] is [tex]\(x \geq -7\)[/tex].
Now, let's check each of the given values against this solution:
- For [tex]\(x = -10\)[/tex]:
[tex]\[
-10 \geq -7 \quad \text{is false}
\][/tex]
- For [tex]\(x = -9\)[/tex]:
[tex]\[
-9 \geq -7 \quad \text{is false}
\][/tex]
- For [tex]\(x = -8\)[/tex]:
[tex]\[
-8 \geq -7 \quad \text{is false}
\][/tex]
- For [tex]\(x = -7\)[/tex]:
[tex]\[
-7 \geq -7 \quad \text{is true}
\][/tex]
Only [tex]\(x = -7\)[/tex] satisfies the inequality. Therefore, 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].
