Final answer:
The inequality 3x + 2 ≤ 5(x - 4) simplifies to x ≥ 11 when solved step-by-step, isolating the variable x. This corresponds to option D, which is the correct answer.
Step-by-step explanation:
To solve the inequality 3x + 2 ≤ 5(x - 4), we must first expand and simplify the equation:
- Expand the right side: 3x + 2 ≤ 5x - 20.
- Subtract 3x from both sides: 2 ≤ 2x - 20.
- Add 20 to both sides: 22 ≤ 2x.
- Finally, divide both sides by 2 to isolate x: 11 ≤ x or x ≥ 11.
This gives us the answer that x is greater than or equal to 11, which matches option D.
The inequality we started with is a linear equation, as it can be rewritten in the form ax + b ≤ c once simplified. During the process, we aim to isolate the variable on one side to find the range of values that satisfy the inequality.