Final answer:
To solve the inequality 3(x – 4) ≥ 5x + 2, distribute 3 and simplify the equation. Subtract 3x, subtract 2, divide by 2 to solve for x. The solution is -7.
Step-by-step explanation:
To solve the inequality 3(x – 4) ≥ 5x + 2, we first distribute 3 to x and -4: 3x - 12 ≥ 5x + 2.
Next, we can subtract 3x from both sides to isolate the variable: -12 ≥ 2x + 2.
Then we subtract 2 from both sides: -14 ≥ 2x.
Finally, we divide both sides by 2 to solve for x: -7 ≥ x.
The correct answer is -7. Therefore, none of the given options (-10, -5, 5, 10) is in the solution set of the inequality.