Let's go through each of the problems one by one and check your answers.
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Solve \(8x > 24\):
To solve this inequality, divide both sides by 8:
\[ x > \frac{24}{8} = 3 \] Your answer: A. \(x > 3\) - Correct.
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Solve \(\frac{x}{13} < \frac{4}{5}\):
To solve for \(x\), multiply both sides by 13:
\[ x < 13 \times \frac{4}{5} = \frac{52}{5} = 10.4 \] Your answer: D. \(x < 10 \frac{2}{5}\) (or \(x < 10.4\)) - Correct.
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Solve the inequality \(4x > 10\):
Divide both sides by 4:
\[ x > \frac{10}{4} = 2.5 \] Your answer: B. Timeline shows an open circle at 2.5 going to the right - Correct.
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You mentioned "open circle at \(1.75\) going left" for \(6x < 10.5\):
To solve \(6x < 10.5\), divide both sides by 6:
\[ x < \frac{10.5}{6} = 1.75 \] So the open circle should be at \(1.75\) and shading goes to the left.
Your answer: Timeline open circle at 1.75 going left - Correct.
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Solve the inequality \(\frac{2}{3}x < 5\):
To isolate \(x\), multiply both sides by \(\frac{3}{2}\):
\[ x < 5 \times \frac{3}{2} = \frac{15}{2} = 7.5 \] This means you should have an open circle at \(7.5\) with shading going to the left.
Your answer: B. Timeline closed circle at 4 going left - This answer is incorrect.
Summary of Answers:
- Correct: \(x > 3\)
- Correct: \(x < 10 \frac{2}{5}\)
- Correct: Open circle at \(2.5\) going to the right
- Correct: Open circle at \(1.75\) going left (because \(x < 1.75\))
- Incorrect: It should be open circle at \(7.5\) going left.
If you have any specific questions about these problems or need further clarification, feel free to ask!