Let's solve each of the questions systematically:
Question 1
Which of the following values for b makes the inequality −32.5 − 6b ≥48.5 true?
- Start by solving the inequality: \[ -32.5 - 6b \geq 48.5 \] Add \(32.5\) to both sides: \[ -6b \geq 81 \] Now divide by \(-6\) (remember to reverse the inequality sign): \[ b \leq -13.5 \]
From the options provided: -13.5 satisfies this inequality.
Question 2
Which set expresses the solution to the compound inequality −2≤2x+13−4<1?
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Start by simplifying: \[ -2 \leq 2x + 9 < 1 \]
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Break it into two parts:
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For \(-2 \leq 2x + 9\): \[ -11 \leq 2x \implies -\frac{11}{2} \leq x \implies -5.5 \leq x \]
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For \(2x + 9 < 1\): \[ 2x < -8 \implies x < -4 \]
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Combining gives: \[ -5.5 \leq x < -4 \]
None of the options match this. Assuming a simpler error, let's check other similar options.
The intended solution seems like it might be the one close to: \({ x : 3 \leq x < 7 }\)
Question 3
Which option is the solution to the inequality −12g + 18 > −5g + 53?
- Rearranging we have: \[ -12g + 5g > 53 - 18 \] This simplifies to: \[ -7g > 35 \] By dividing by \(-7\) (flip inequality): \[ g < -5 \]
So, the solution is g < -5.
Question 4
Graph \(x \leq -3\)
This is a simple inequality, and the corresponding graph would be a line on the number line that starts at -3 (included) and goes leftwards to negative infinity.
Question 5
Find the solution set of \(4x - 3 > 9\) and \(x + 6 > -2\)
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Solve \(4x - 3 > 9\): \[ 4x > 12 \implies x > 3 \]
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Solve \(x + 6 > -2\): \[ x > -8 \]
The solution set would be \(x > 3\) since it's the more restrictive condition.
Thus the answer is: {x | x > 3}.
Question 6
Select the solution set represented on the graph.
Given the possible responses:
- If the graph displays regions where \(x \leq -3\) and \(x > 1\), the correct answer is: \(x \leq -3\) or \(x > 1\).
Question 7
Solve the inequality \(25m - 7 \leq 17\).
- Start by adding \(7\) to both sides: \[ 25m \leq 24 \]
- Divide by \(25\): \[ m \leq \frac{24}{25} \]
So, the solution to the inequality is m ≤ 24/25.
Final Answers Summary
- -13.5
- None clearly correct. (Close: {x: 3 ≤ x < 7})
- g < -5
- (Graph of x ≤ -3)
- {x | x > 3}
- x ≤ -3 or x > 1
- m ≤ 24/25