Question

What value of x is in the solution set of 2(3x – 1) ≥ 4x – 6?

a) x ≤ 2
b) x ≥ 2
c) x ≤ -2
d) x ≥ -2

Answer 1

To find the value of x in the solution set of the inequality 2(3x – 1) ≥ 4x – 6, we simplify and solve the inequality to find that x ≥ -2, which matches option d).

Step-by-step explanation:

To solve the inequality 2(3x – 1) ≥ 4x – 6, we first expand the left side:

6x - 2 ≥ 4x - 6

Next, we move all x terms to one side and the constant terms to the opposite side:

6x - 4x ≥ -6 + 2

Which simplifies to:

2x ≥ -4

Dividing both sides of the inequality by 2 gives us:

x ≥ -2

Thus, the value of x that satisfies the inequality is x ≥ -2, which corresponds to option d).