To solve the inequality [tex]\( 4(-2x + 1) \geq -12 \)[/tex], let's follow a step-by-step approach:
1. Distribute the 4:
[tex]\[
4 \cdot (-2x + 1) \geq -12
\][/tex]
This simplifies to:
[tex]\[
4 \cdot (-2x) + 4 \cdot 1 \geq -12
\][/tex]
[tex]\[
-8x + 4 \geq -12
\][/tex]
2. Isolate the term involving [tex]\(x\)[/tex]:
To isolate the term involving [tex]\(x\)[/tex], subtract 4 from both sides of the inequality:
[tex]\[
-8x + 4 - 4 \geq -12 - 4
\][/tex]
Simplifying this gives:
[tex]\[
-8x \geq -16
\][/tex]
3. Solve for [tex]\(x\)[/tex]:
To solve for [tex]\(x\)[/tex], divide both sides by -8. Remember, when you divide by a negative number, the inequality sign flips:
[tex]\[
\frac{-8x}{-8} \leq \frac{-16}{-8}
\][/tex]
Simplifying this gives:
[tex]\[
x \leq 2
\][/tex]
So, the correct choice is:
A. The solution is [tex]\( x \leq 2 \)[/tex]
