Question

Solve the compound inequality statement. -5 < -2x + 3 ≤ 12

Answer 1

The solution to the compound inequality -5 < -2x + 3 ≤ 12 is -4.5 ≤ x < 4, which requires subtracting 3 from all parts and then dividing by -2, while also reversing the inequality signs.

Step-by-step explanation:

To solve the compound inequality -5 < -2x + 3 ≤ 12, we need to isolate x in the middle of the inequality. We'll do this in two steps:

1. Subtract 3 from all three parts to get -8 < -2x ≤ 9.
2. Divide all parts by -2, remembering to reverse the inequality signs because we are dividing by a negative number. This gives us 4 > x ≥ -4.5 or -4.5 ≤ x < 4 when we write it in the more conventional order.

The solution to the compound inequality is x is greater than or equal to -4.5 and less than 4.

To represent this on a number line, you would draw a closed circle at -4.5 and an open circle at 4, with a shaded line connecting them to indicate that all numbers between these two values are included.