Question

Solve for (z). Reduce any tions to the lowest terms. Don't round your answer, and don't use mixed tions. (-4z + 31 ≥ 17z + 23)

A. (z ≤ 8/21)
B. (z ≥ 8/21)
C. (z ≤ 21/8)
D. (z ≥ 21/8)

Answer 1

The inequality −4z + 31 ≥ 17z + 23 is solved by combining like terms and then isolating z, leading to the final solution of z ≤ 8/21, which is option A.

Step-by-step explanation:

The question involves solving an inequality in one variable. Here is the step-by-step solution:

1. Start with the inequality −4z + 31 ≥ 17z + 23.
2. Combine like terms by adding 4z to both sides to get 31 ≥ 21z + 23.
3. Next, subtract 23 from both sides, resulting in 8 ≥ 21z.
4. Divide both sides by 21 to isolate z, giving ≤ 8/21.
5. Finally, flip the inequality when dividing by a positive number, so the correct answer is z ≤ 8/21, which corresponds to option A: (z ≤ 8/21).

This solution is reasonable since it was found by applying basic algebraic operations to manipulate the inequality, ensuring lowest terms and checking that the final result is in line with expectation based on known mathematical rules.