Final answer:
The inequality -24 ≤ -3 - 8x is solved by isolating the variable x, which leads to the solution x ≤ 21/8 or x ≤ 2.625, none of the options provided in the question are correct.
Step-by-step explanation:
The student is asked to solve the inequality -24 ≤ -3 - 8x. To solve for x, we first isolate the x variable on one side of the inequality:
- Add 3 to both sides: -24 + 3 ≤ -8x, which simplifies to -21 ≤ -8x.
- Divide both sides by -8, remembering to reverse the inequality sign because we are dividing by a negative number: 21/8 ≥ x, or x ≤ 21/8.
The solution to the inequality is x ≤ 21/8, which simplifies to x ≤ 2.625. Therefore, none of the given options (a) x > 3, (b) x ≤ 3, (c) x² - 3, (d) x ≥ -9 is correct.