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

Question

−8x + 6 ≤ 2(−3x + 1)
Responses
A x ≥ 2 x ≥ 2
B x ≤ 2 x ≤ 2
C x > 12
x > 1 2
D x < −1

Answer 1

To solve this inequality, we can start by simplifying both sides of the equation:
-8x + 6 ≤ 2(-3x + 1)

Distributing the 2 on the right side, we get:
-8x + 6 ≤ -6x + 2

Next, we can combine like terms on both sides:
-8x + 6 + 8x ≤ -6x + 2 + 8x
6 ≤ 2x + 2

Subtracting 2 from both sides:
6 - 2 ≤ 2x + 2 - 2
4 ≤ 2x

Lastly, we divide both sides by 2 to isolate x:
4/2 ≤ 2x/2
2 ≤ x

Therefore, all the possible values of x that satisfy the inequality are x ≥ 2.

So, the correct answer is A) x ≥ 2.