Question

Solve the compound inequality (-19 ≤5-3x ≤520).

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A. The solution set is (-174/3, 175)
B. The solution set is Ø

Answer 1

To solve the compound inequality (-19 ≤ 5-3x ≤ 520), solve the two separate inequalities: -24 ≤ -3x and 0 ≤ -3x+515. The solution set is 8 ≥ x ≤ 171.667, which means the solution set is Ø (empty set).

Step-by-step explanation:

To solve the compound inequality (-19 ≤ 5-3x ≤ 520), we need to solve the two separate inequalities: -19 ≤ 5-3x and 5-3x ≤ 520. Let's solve each inequality step by step:

First inequality:

Subtract 5 from both sides: -24 ≤ -3x

Divide both sides by -3, remembering to reverse the inequality sign: 8 ≥ x

Second inequality:

Subtract 5 from both sides: 0 ≤ -3x+515

Subtract 515 from both sides: -515 ≤ -3x

Divide both sides by -3, remembering to reverse the inequality sign: x ≤ 171.667

So, the solution set is: 8 ≥ x ≤ 171.667. Therefore, the correct choice is B. The solution set is Ø (empty set).