To solve the inequality [tex]\(-4(8 - 3x) \geq 6x - 8\)[/tex], let's follow a step-by-step process:
1. Distribute the [tex]\(-4\)[/tex] on the left side of the inequality:
[tex]\[
-4(8 - 3x) \geq 6x - 8
\][/tex]
This gives us:
[tex]\[
-4 \cdot 8 + (-4) \cdot (-3x) \geq 6x - 8
\][/tex]
Simplifying further:
[tex]\[
-32 + 12x \geq 6x - 8
\][/tex]
2. Combine like terms:
To simplify, let's move all the terms involving [tex]\(x\)[/tex] to one side and constant terms to the other side. Subtract [tex]\(6x\)[/tex] from both sides:
[tex]\[
-32 + 12x - 6x \geq -8
\][/tex]
Simplifying, we get:
[tex]\[
-32 + 6x \geq -8
\][/tex]
3. Isolate the [tex]\(x\)[/tex] term:
Now, add 32 to both sides to isolate the [tex]\(x\)[/tex] term:
[tex]\[
-32 + 6x + 32 \geq -8 + 32
\][/tex]
Simplifying, we have:
[tex]\[
6x \geq 24
\][/tex]
4. Solve for [tex]\(x\)[/tex]:
Finally, divide both sides by 6:
[tex]\[
x \geq \frac{24}{6}
\][/tex]
Which simplifies to:
[tex]\[
x \geq 4
\][/tex]
So, the solution to the inequality [tex]\(-4(8 - 3x) \geq 6x - 8\)[/tex] is:
[tex]\[
x \geq 4
\][/tex]
The correct answer is:
[tex]\[ x \geq 4 \][/tex]
