1.
Item 1. Solve \(16-5x=3x\).
Solution:\(16-5x=3x\)Add \(5x\) to both sides:\(16=8x\)Divide both sides by \(8\):\(x=2\)Answer: C
2.
Item 3. Identify the appropriate inequality that represents the graph on the number line.
Solution:The number line has a closed dot at \(-1\), so \(-1\) is included in the solution.The arrow goes to the right, so the solution is greater than \(-1\).Therefore, the inequality is:\(x\ge -1\)Answer: D
3.
Item 5. Solve the following for \(x\): \(2(x-2)\ge 3(2-x)\).
Solution:\(2(x-2)\ge 3(2-x)\)Distribute:\(2x-4\ge 6-3x\)Add \(3x\) to both sides:\(5x-4\ge 6\)Add \(4\) to both sides:\(5x\ge 10\)Divide by \(5\):\(x\ge 2\)Answer: C
4.
Item 6. Which of the following is the correct interval notation for the given number line?
Solution:The solution has only one region, so the final answer has one interval.The endpoints are \(0\) and \(8\).The left endpoint \(0\) has a closed circle, so \(0\) is included and we use a square bracket: \([\).The right endpoint \(8\) has an open circle, so \(8\) is not included and we use a round parenthesis: \()\).Therefore, the interval notation is:\([0,8)\)Answer: E
5.
Item 2. Solve \(7+3(2x-1)=-9-4(x+1)\).
Solution:\(7+3(2x-1)=-9-4(x+1)\)Distribute:\(7+6x-3=-9-4x-4\)Simplify both sides:\(6x+4=-4x-13\)Add \(4x\) to both sides:\(10x+4=-13\)Subtract \(4\) from both sides:\(10x=-17\)Divide by \(10\):\(x=-\frac{17}{10}=-1\frac{7}{10}\)Answer: A
6.
Item 4. Solve \(3-4x
Solution:\(3-4x<15\)Subtract \(3\) from both sides:\(-4x<12\)Divide both sides by \(-4\). Since we divide by a negative number, reverse the inequality sign:\(x>-3\)Answer: B
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