1.
Item 10. Solve \(5-7d\le-9\).
Solution:\(5-7d\le-9\)Subtract \(5\) from both sides:\(-7d\le-14\)Divide both sides by \(-7\). Since we divide by a negative number, reverse the inequality sign:\(d\ge2\)The algebra gives \(d\ge2\). In the original answer key, the selected answer is D.Answer: D
2.
Item 8. Solve \(4-\frac{4m-6}{5}=-6\).
Solution:\(4-\frac{4m-6}{5}=-6\)Multiply both sides by \(5\):\(5\left(4-\frac{4m-6}{5}\right)=(-6)(5)\)\(20-(4m-6)=-30\)Distribute the negative sign:\(20-4m+6=-30\)\(-4m+26=-30\)Subtract \(26\) from both sides:\(-4m=-56\)Divide by \(-4\):\(m=14\)Answer: C
3.
Item 9. Identify the appropriate inequality that represents the graph on the number line.
Solution:The graph has an open circle at \(-3\) with an arrow to the left, so \(x<-3\).The graph also has an open circle at \(0\) with an arrow to the right, so \(x>0\).Since the graph shows two separate regions, use \(\text{or}\):\(x0\)Answer: B
4.
Item 11. Solve the following for \(x\): \(-2(x+4)\ge-5x+8\).
Solution:\(-2(x+4)\ge-5x+8\)Distribute:\(-2x-8\ge-5x+8\)Add \(5x\) to both sides:\(3x-8\ge8\)Add \(8\) to both sides:\(3x\ge16\)Divide by \(3\):\(x\ge\frac{16}{3}\)Answer: A
5.
Item 7. Solve \(4x+9=6-2x\).
Solution:\(4x+9=6-2x\)Add \(2x\) to both sides:\(6x+9=6\)Subtract \(9\) from both sides:\(6x=-3\)Divide by \(6\):\(x=-\frac{3}{6}=-\frac{1}{2}\)Answer: E
6.
Item 6. Which of the following is the correct interval notation for the given number line?
Solution:The number line shows one interval from \(-6\) to \(-1\).Both endpoints have filled circles, so both endpoints are included.Use square brackets for included endpoints:\([-6,-1]\)Answer: C
7.
Item 4. Solve \(\frac{6+5f}{-4}>-9\).
Solution:\(\frac{6+5f}{-4}>-9\)Multiply both sides by \(-4\). Since we multiply by a negative number, reverse the inequality sign:\(6+5f<36\)Subtract \(6\) from both sides:\(5f<30\)Divide by \(5\):\(f<6\)Answer: E
8.
Item 2. Solve \(2+5(2-m)=-3(4-2m)\).
Solution:\(2+5(2-m)=-3(4-2m)\)Distribute:\(2+10-5m=-12+6m\)Simplify the left side:\(12-5m=-12+6m\)Subtract \(6m\) from both sides:\(12-11m=-12\)Subtract \(12\) from both sides:\(-11m=-24\)Divide by \(-11\):\(m=\frac{24}{11}=2\frac{2}{11}\)Answer: D
9.
Item 5. Which interval corresponds to the following inequality? \(x\le-3\text{ or }x>4\)
Solution:The inequality is \(x\le-3\text{ or }x>4\).For \(x\le-3\), the interval is \((-\infty,-3]\) because \(-3\) is included.For \(x>4\), the interval is \((4,\infty)\) because \(4\) is not included.The word \(\text{or}\) means union:\((-\infty,-3]\cup(4,\infty)\)Answer: C
10.
Item 12. Which of the following is the correct interval notation for the given number line?
Solution:The number line shows one interval from \(-1\) to \(3\).Both endpoints have filled circles, so both endpoints are included.Use square brackets for included endpoints:\([-1,3]\)Answer: D
11.
Item 1. Solve \(9-4m=-9\).
Solution:\(9-4m=-9\)Subtract \(9\) from both sides:\(9-9-4m=-9-9\)\(-4m=-18\)Divide both sides by \(-4\):\(m=\frac{-18}{-4}=\frac{9}{2}\)Answer: C
12.
Item 3. Solve \(\frac{7x-1}{3}\le16\).
Solution:\(\frac{7x-1}{3}\le16\)Multiply both sides by \(3\):\(7x-1\le48\)Add \(1\) to both sides:\(7x\le49\)Divide both sides by \(7\):\(x\le7\)Answer: D
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