To determine which value of [tex]\(x\)[/tex] satisfies the inequality [tex]\(4x - 12 \leq 16 + 8x\)[/tex], we will solve the inequality step by step.
1. Start with the original inequality:
[tex]\[
4x - 12 \leq 16 + 8x
\][/tex]
2. Subtract [tex]\(4x\)[/tex] from both sides to isolate the variable [tex]\(x\)[/tex] on one side:
[tex]\[
-12 \leq 16 + 4x
\][/tex]
3. Subtract 16 from both sides to further isolate the term involving [tex]\(x\)[/tex]:
[tex]\[
-28 \leq 4x
\][/tex]
4. Divide both sides by 4 to solve for [tex]\(x\)[/tex]:
[tex]\[
-7 \leq x
\][/tex]
This can also be written as:
[tex]\[
x \geq -7
\][/tex]
Now we need to check which of the given values satisfies [tex]\(x \geq -7\)[/tex]:
- For [tex]\(x = -10\)[/tex]:
[tex]\[
-10 \not\geq -7 \quad \Rightarrow \text{Not a solution}
\][/tex]
- For [tex]\(x = -9\)[/tex]:
[tex]\[
-9 \not\geq -7 \quad \Rightarrow \text{Not a solution}
\][/tex]
- For [tex]\(x = -8\)[/tex]:
[tex]\[
-8 \not\geq -7 \quad \Rightarrow \text{Not a solution}
\][/tex]
- For [tex]\(x = -7\)[/tex]:
[tex]\[
-7 \geq -7 \quad \Rightarrow \text{Solution}
\][/tex]
Therefore, the value in the solution set of the inequality [tex]\(4x - 12 \leq 16 + 8x\)[/tex] is:
[tex]\[
-7
\][/tex]
