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------------------------------------------------ 9. Which of the following represents the solution set to the inequality [tex]2(2-4x) + 3(2x+6) \ \textless \ 8[/tex]?

A. [tex]x \geq 15[/tex]

B. [tex]x \leq 15[/tex]

C. [tex]x \ \textgreater \ 7[/tex]

D. [tex]x \ \textless \ 7[/tex]

Sure! Let's solve the inequality step-by-step to find the solution set for [tex]\(2(2 - 4x) + 3(2x + 6) < 8\)[/tex].

1. Expand the expressions:
- Distribute the 2 in the first term: [tex]\(2 \times (2 - 4x) = 4 - 8x\)[/tex]
- Distribute the 3 in the second term: [tex]\(3 \times (2x + 6) = 6x + 18\)[/tex]

2. Write the expanded inequality:
[tex]\[
4 - 8x + 6x + 18 < 8
\][/tex]

3. Combine like terms:
- Combine the constant terms: [tex]\(4 + 18 = 22\)[/tex]
- Combine the [tex]\(x\)[/tex] terms: [tex]\(-8x + 6x = -2x\)[/tex]

So, the inequality becomes:
[tex]\[
22 - 2x < 8
\][/tex]

4. Isolate the [tex]\(x\)[/tex] term:
- Subtract 22 from both sides:
[tex]\[
-2x < 8 - 22
\][/tex]
[tex]\[
-2x < -14
\][/tex]

5. Solve for [tex]\(x\)[/tex]:
- Divide both sides by -2, and remember to reverse the inequality sign when you divide by a negative number:
[tex]\[
x > 7
\][/tex]

Therefore, the solution set for the inequality is [tex]\(x > 7\)[/tex].

The correct answer is c. [tex]\(x > 7\)[/tex].