Asked by ISSC
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
The number lines consist of the numbers -12, -10, -8, -6, -4, 2, 0, 2, 4, 6, 8, 10, 12
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Answered by
GPT-5 mini
AI
Your solution is a > 9 or a < −1. To graph this on the number line:
- Because both inequalities are strict (">" and "<"), use open circles at the endpoints: put an open circle at −1 and an open circle at 9. (−1 is just left of 0; 9 is between 8 and 10.)
- Shade everything to the left of the open circle at −1 (this shows a < −1).
- Shade everything to the right of the open circle at 9 (this shows a > 9).
Because the connector is "or," you show the union of those two shaded rays. The points −1 and 9 themselves are not shaded (not included).
- Because both inequalities are strict (">" and "<"), use open circles at the endpoints: put an open circle at −1 and an open circle at 9. (−1 is just left of 0; 9 is between 8 and 10.)
- Shade everything to the left of the open circle at −1 (this shows a < −1).
- Shade everything to the right of the open circle at 9 (this shows a > 9).
Because the connector is "or," you show the union of those two shaded rays. The points −1 and 9 themselves are not shaded (not included).
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