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

Question

−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 this inequality, we can start by distributing the 2 on the right side of the equation:

−8x + 6 ≤ 2(−3x + 1)
−8x + 6 ≤ −6x + 2

Next, let's move all the x terms to one side and all the constant terms to the other side:

−8x + 6 + 6x ≤ −6x + 2 + 6x
−2x + 6 ≤ 2

Now, let's subtract 6 from both sides:

−2x + 6 - 6 ≤ 2 - 6
−2x ≤ -4

Finally, let's divide both sides by -2. However, since we are dividing by a negative number, the inequality sign flips:

x ≥ 2

So, the solution to the inequality is x ≥ 2.

Therefore, the correct answer is A) x ≥ 2.