Question

What value of x is in the solution set of

3(x - 4) ≥ 5x + 2

O -10
O -5
O 5
O 10

Answer 1

The value of x that satisfies the inequality 3(x - 4) ≥ 5x + 2 is x ≤ -7. Out of the choices given, -10 is the only value that fits the solution set, as it is less than or equal to -7.

Step-by-step explanation:

The question is asking for the value of x that satisfies the inequality 3(x - 4) ≥ 5x + 2. To find the solution, we first expand the left side and then isolate the variable x to one side of the inequality.

1. Multiply out the left side: 3x - 12 ≥ 5x + 2.
2. Move all terms with x to one side and constants to the other side: -2x ≥ 14.
3. Divide both sides by -2, remembering to switch the direction of the inequality sign because we are dividing by a negative number: x ≤ -7.

None of the provided options (-10, -5, 5, 10) are equal to -7; however, the question is looking for a value that is within the solution set. Since x ≤ -7, we look for the value that is less than or equal to -7. Out of the provided options, -10 is in the solution set.