Question

In the inequality, what are all the possible values of x?

−8x + 6 ≤ 2(−3x + 1)
Responses
A x ≥ 2x ≥ 2
B x ≤ 2x ≤ 2
C x >


x > 1/2
D x < −1

Answer 1

To solve the inequality \(-8x + 6 \leq 2(-3x + 1)\), let's start by simplifying the right side:

1. Distribute \(2\) on the right:
\[
2(-3x + 1) = -6x + 2
\]

2. Now, rewrite the original inequality:
\[
-8x + 6 \leq -6x + 2
\]

3. Next, let's isolate \(x\). Start by adding \(6x\) to both sides:
\[
-8x + 6 + 6x \leq 2
\]
This simplifies to:
\[
-2x + 6 \leq 2
\]

4. Now, subtract \(6\) from both sides:
\[
-2x \leq 2 - 6
\]
This simplifies to:
\[
-2x \leq -4
\]

5. Divide both sides by \(-2\), remembering to reverse the inequality sign:
\[
x \geq 2
\]

Thus, the solution to the inequality is:
\[
\boxed{x \geq 2}
\]

Therefore, the correct response is:
**A \(x \geq 2\)**.