Let's go through each of your problems and check your answers.
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Solve 8x > 24
- To solve for x: \[ x > \frac{24}{8} \implies x > 3 \]
- Your answer: A. \( x > 3 \) (Correct)
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Solve \( \frac{x}{13} < \frac{4}{5} \)
- To solve for x: \[ x < 13 \times \frac{4}{5} \implies x < \frac{52}{5} \implies x < 10.4 \]
- Your answer: D. \( x < 10 \frac{2}{5} \) (Incorrect, should be \( x < 10.4 \) or \( x < 10.8 \))
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Solve inequality 4x > 10
- To solve for x: \[ x > \frac{10}{4} \implies x > 2.5 \]
- Your answer: B. Open circle at 2.5 going to the right (Correct)
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Open circle at 1.75 going left, your answer is \( 6x < 10.5 \) doesn't appear to match the inequality context. If the inequality were instead something like \( x < 1.75 \):
- Solve for that: \[ x < 1.75 \]
- This would give an open circle at 1.75 going left (it seems you may need to check the actual inequality).
- Your answer: Could be correct if the inequality were something less than 1.75, but needs context.
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Solve inequality \( \frac{2}{3}x < 5 \)
- Multiply both sides by \( \frac{3}{2} \): \[ x < \frac{5 \times 3}{2} \implies x < 7.5 \]
- If the solution were represented on a timeline, it would be a closed circle at 7.5 or less on the left (it seems you might need to adjust this).
- Your answer for the timeline: B. Timeline closed circle on the right of 4 going left (Incorrect)
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Identifying Timeline answers:
- If you're asked to identify timeline options, remember that:
- Open circles indicate "not including" that point.
- Closed circles indicate including that point.
- Ensure you match the inequalities to the correct visuals provided.
- If you're asked to identify timeline options, remember that:
Overall, your answers seem accurate for the first one, but the others need revisions or clarifications. Make sure to recheck the inequalities for correct directions and answers against provided visual aids.