Final answer:
To find the solutions for the compound inequality -17.5 ≤ -17.5 < (2x + 4)/3 < 17.5, we need to solve each inequality separately and find the overlapping solutions. The solutions for the compound inequality are -28.25 < x < 24.25. The only number that falls within this range is -2.25, so option 4) -2.25 is the solution.
Step-by-step explanation:
To find the solutions for the compound inequality -17.5 ≤ -17.5 < (2x + 4)/3 < 17.5, we need to solve each inequality separately and find the overlapping solutions. Let's start:
-17.5 ≤ -17.5: This inequality is always true, so it doesn't restrict the possible solutions.
-17.5 < (2x + 4)/3: Multiply both sides by 3 to get rid of the denominator, giving -52.5 < 2x + 4. Subtract 4 from both sides to isolate 2x, resulting in -56.5 < 2x. Divide both sides by 2 to solve for x, giving -28.25 < x.
(2x + 4)/3 < 17.5: Multiply both sides by 3 to get rid of the denominator, resulting in 2x + 4 < 52.5. Subtract 4 from both sides to isolate 2x, giving 2x < 48.5. Divide both sides by 2 to solve for x, resulting in x < 24.25.
So, the solutions for the compound inequality are -28.25 < x < 24.25. Looking at the given options, the only number that falls within this range is -2.25, so option 4) -2.25 is the solution.