Question

Solve 29<(m^2+9)/2<45

Answer 1

Answer:

  -9 < m < -7 ∪ 7 < m < 9

Step-by-step explanation:

You can proceed in the usual way up to the point where you need to take the square root.

Multiply by 2:

  58 < m^2 +9 < 90

Subtract 9:

  49 < m^2 < 81

Take the square root:

  7 < |m| < 9

This resolves to two sets of inequalities:

  7 < -m < 9   ⇒   -9 < m < -7

  7 < m < 9

The solution set is the union of these intervals: (-9, -7) ∪ (7, 9).