Question

Solve the compound inequality:

2x - 3 < 7 and 5 - x ≤ 8.

a) x ≥ 3 and x < 2
b) x ≥ 3 and x < 5
c) x ≥ -3 and x < 2
d) x ≥ -3 and x < 5

Answer 1

The solution to the compound inequality is to solve each part separately and then find the overlap. The correct answer is (d) x ≥ -3 and x < 5, as x must be greater than or equal to -3 and less than 5.

Step-by-step explanation:

To solve the compound inequality, we need to address each part of the inequality separately and then find the intersection of the solutions.

First solve 2x - 3 < 7:

1. Add 3 to both sides: 2x < 10
2. Divide by 2: x < 5

Then solve 5 - x ≤ 8:

1. Subtract 5 from both sides: -x ≤ 3
2. Multiply by -1 and reverse the inequality sign: x ≥ -3

We now combine the solutions: x must be greater than or equal to -3 and less than 5. This is represented by the inequality -3 ≤ x < 5.

So the correct answer is (d) x ≥ -3 and x < 5.