Question

one step inequalities - addition/subtraction - scavenger hunt worksheet
name: kamarcus harris
solve and graph #1. then find the matching graph, which is the next problem.
continue until you complete the worksheet. label number lines and show all work.
start (show all work)
solve: ( x + 4 < - 3 )
graph:
write problem numbers here.
if you found:
solve: ( 4 geq x + 7 )
graph:
if you found:
solve: ( 3 + x > 2 )
graph:
solve: ( x - 3 geq 3 )
graph:
solve: ( 6 geq 7 + x )
graph:
solve: ( x + 8 geq 5 )
graph:
solve: ( 3 leq x + 10 )
graph:
solve: ( 3 < - 1 + x )
graph:
solve: ( x - 10 < - 4 )
graph:
solve: ( 3 + x < 3 )
graph:
solve: ( - 5 + x > 1 )
graph:
solve: ( - 3 leq x - 7 )
graph:

Explanation:

Step1: Solve \(x - 3\geq3\)

Add \(3\) to both sides of the inequality.
\(x-3 + 3\geq3 + 3\)
\(x\geq6\)

Step2: Graph \(x\geq6\)

On the number - line, put a closed circle at \(6\) (because the inequality includes equality, i.e., \(x = 6\) is a solution) and shade to the right (since \(x\) is greater than or equal to \(6\)).

Step3: Solve \(6\geq7 + x\)

Subtract \(7\) from both sides.
\(6-7\geq7 + x-7\)
\(- 1\geq x\) or \(x\leq - 1\)

Step4: Graph \(x\leq - 1\)

On the number - line, put a closed circle at \(-1\) (because the inequality includes equality) and shade to the left.

Step5: Solve \(x + 8\geq5\)

Subtract \(8\) from both sides.
\(x+8 - 8\geq5 - 8\)
\(x\geq - 3\)

Step6: Graph \(x\geq - 3\)

On the number - line, put a closed circle at \(-3\) (because the inequality includes equality) and shade to the right.

Step7: Solve \(3\lt - 1+x\)

Add \(1\) to both sides.
\(3 + 1\lt-1+x + 1\)
\(4\lt x\) or \(x\gt4\)

Step8: Graph \(x\gt4\)

On the number - line, put an open circle at \(4\) (because the inequality does not include equality) and shade to the right.

Step9: Solve \(3 + x\lt3\)

Subtract \(3\) from both sides.
\(3 + x-3\lt3 - 3\)
\(x\lt0\)

Step10: Graph \(x\lt0\)

On the number - line, put an open circle at \(0\) (because the inequality does not include equality) and shade to the left.

Step11: Solve \(-3\leq x - 7\)

Add \(7\) to both sides.
\(-3+7\leq x - 7+7\)
\(4\leq x\) or \(x\geq4\)

Step12: Graph \(x\geq4\)

On the number - line, put a closed circle at \(4\) (because the inequality includes equality) and shade to the right.

Answer:

• For \(x - 3\geq3\): \(x\geq6\), graph with closed circle at \(6\) and shade right.
• For \(6\geq7 + x\): \(x\leq - 1\), graph with closed circle at \(-1\) and shade left.
• For \(x + 8\geq5\): \(x\geq - 3\), graph with closed circle at \(-3\) and shade right.
• For \(3\lt - 1+x\): \(x\gt4\), graph with open circle at \(4\) and shade right.
• For \(3 + x\lt3\): \(x\lt0\), graph with open circle at \(0\) and shade left.
• For \(-3\leq x - 7\): \(x\geq4\), graph with closed circle at \(4\) and shade right.