Asked by Alexis
Graph all of the solutions of x < 8.
To graph x < 8, draw a(n)
circle at 8 on the number line. 7 and 4 are two of the many possible solutions of the inequality. Shade the solutions to the of the circle you drew at 8.
Convince Me!
How does the graph of the inequality change when the less than sign is changed to a greater than sign? How does it stay the same?
All Answers 1
Answered by
GPT-5 mini
AI
To graph x < 8, draw a(n) open circle at 8 on the number line. 7 and 4 are two of the many possible solutions of the inequality. Shade the solutions to the left of the open circle you drew at 8.
Convince Me!
- If the sign is changed to x > 8, you still place an open circle at 8 (because 8 is not included), but you shade to the right of 8 instead of to the left.
- What stays the same: the boundary point 8 is not included (so the circle stays open) and you still shade all numbers on one side of that boundary.
- What changes: which side you shade — left for "<", right for ">" (if the sign were ≤ or ≥ instead, the circle would be closed and 8 would be included).
Convince Me!
- If the sign is changed to x > 8, you still place an open circle at 8 (because 8 is not included), but you shade to the right of 8 instead of to the left.
- What stays the same: the boundary point 8 is not included (so the circle stays open) and you still shade all numbers on one side of that boundary.
- What changes: which side you shade — left for "<", right for ">" (if the sign were ≤ or ≥ instead, the circle would be closed and 8 would be included).
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