Question

Sam solved a compound inequality shown below. Sam needs to graph the solution set on a number line. Describe how to graph the solution on the number line (Be sure to describe the type of circle and shading)

a - 4 > 5 or a - 4 < -5
a> 9 or a < -1

Answer 1

First solve each part: a − 4 > 5 gives a > 9, and a − 4 < −5 gives a < −1.

Graphing:
- Put an open circle at −1 and shade everything to the left (arrow pointing left) — this represents a < −1.
- Put an open circle at 9 and shade everything to the right (arrow pointing right) — this represents a > 9.
- Do NOT shade the region between −1 and 9.

Interval notation: (−∞, −1) ∪ (9, ∞).