Question

one step inequalities - addition/subtraction - scavenger hunt worksheet
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.
name:
start (show all work)
solve: $x + 4 < -3$
graph:
1 write problem numbers here.
if you found:
solve: $4 \geq x + 7$
graph:
if you found:
solve: $3 + x > 2$
graph:
if you found:
solve: $x - 3 \geq 3$
graph:
if you found:
solve: $6 \geq 7 + x$
graph:
if you found:
solve: $x + 8 \geq 5$
graph:
if you found:
solve: $3 \leq x + 10$
graph:
if you found:
solve: $3 < -1 + x$
graph:
if you found:
solve: $x - 10 < -4$
graph:
if you found:
solve: $3 + x < 3$
graph:
if you found:
solve: $-5 + x > 1$
graph:
if you found:
solve: $-3 \leq x - 7$
graph:

Explanation:

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

Add \(3\) to both sides of the inequality \(x - 3\geq3\).
Using the addition property of inequalities (\(a\geq b\Rightarrow a + c\geq b + c\)), we get \(x-3 + 3\geq3 + 3\), which simplifies to \(x\geq6\).

Step2: Graph \(x\geq6\)

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

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

Subtract \(7\) from both sides of the inequality \(6\geq7 + x\).
Using the subtraction property of inequalities (\(a\geq b\Rightarrow a - c\geq b - c\)), we get \(6-7\geq7 + x-7\), which simplifies to \(-1\geq x\) or \(x\leq - 1\).

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

On a number - line, we draw a closed circle at \(-1\) (because the inequality includes equality, i.e., \(x=-1\) is a solution) and draw an arrow to the left (since \(x\) is less than or equal to \(-1\)).

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

Subtract \(8\) from both sides of the inequality \(x + 8\geq5\).
Using the subtraction property of inequalities (\(a\geq b\Rightarrow a - c\geq b - c\)), we get \(x+8 - 8\geq5 - 8\), which simplifies to \(x\geq - 3\).

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

On a number - line, we draw a closed circle at \(-3\) (because the inequality includes equality, i.e., \(x = - 3\) is a solution) and draw an arrow to the right (since \(x\) is greater than or equal to \(-3\)).

Step7: Solve \(3\leq x + 10\)

Subtract \(10\) from both sides of the inequality \(3\leq x + 10\).
Using the subtraction property of inequalities (\(a\leq b\Rightarrow a - c\leq b - c\)), we get \(3-10\leq x + 10-10\), which simplifies to \(x\geq - 7\).

Step8: Graph \(x\geq - 7\)

On a number - line, we draw a closed circle at \(-7\) (because the inequality includes equality, i.e., \(x=-7\) is a solution) and draw an arrow to the right (since \(x\) is greater than or equal to \(-7\)).

Step9: Solve \(3\lt - 1+x\)

Add \(1\) to both sides of the inequality \(3\lt - 1+x\).
Using the addition property of inequalities (\(a\lt b\Rightarrow a + c\lt b + c\)), we get \(3 + 1\lt-1+x + 1\), which simplifies to \(x\gt4\).

Step10: Graph \(x\gt4\)

On a number - line, we draw an open circle at \(4\) (because the inequality does not include equality, i.e., \(x = 4\) is not a solution) and draw an arrow to the right (since \(x\) is greater than \(4\)).

Step11: Solve \(x-10\lt - 4\)

Add \(10\) to both sides of the inequality \(x-10\lt - 4\).
Using the addition property of inequalities (\(a\lt b\Rightarrow a + c\lt b + c\)), we get \(x-10 + 10\lt-4 + 10\), which simplifies to \(x\lt6\).

Step12: Graph \(x\lt6\)

On a number - line, we draw an open circle at \(6\) (because the inequality does not include equality, i.e., \(x = 6\) is not a solution) and draw an arrow to the left (since \(x\) is less than \(6\)).

Step13: Solve \(3 + x\lt3\)

Subtract \(3\) from both sides of the inequality \(3 + x\lt3\).
Using the subtraction property of inequalities (\(a\lt b\Rightarrow a - c\lt b - c\)), we get \(3 + x-3\lt3 - 3\), which simplifies to \(x\lt0\).

Step14: Graph \(x\lt0\)

On a number - line, we draw an open circle at \(0\) (because the inequality does not include equality, i.e., \(x = 0\) is not a solution) and draw an arrow to the left (since \(x\) is less than \(0\)).

Step15: Solve \(-5 + x\gt1\)

Add \(5\) to both sides of the inequality \(-5 + x\gt1\).
Using the addition property of inequalities (\(a\gt b\Rightarrow a + c\gt b + c\)), we get \(-5 + x+5\gt1 + 5\), which simplifies to \(x\gt6\).

Step16: Graph \(x\gt6\)

On a number - line, we draw an open circle at \(6\) (because the inequality does not include equality, i.e., \(x = 6\) is not a solution) and draw an arrow to the right (since \(x\) is greater than \(6\)).

Step17: Solve \(-3\leq x-7\)

Add \(7\) to both sides of the inequality \(-3\leq x-7\).
Using the addition property of inequalities (\(a\leq b\Rightarrow a + c\leq b + c\)), we get \(-3 + 7\leq x-7 + 7\), which simplifies to \(x\geq4\).

Step18: Graph \(x\geq4\)

On a number - line, we draw a closed circle at \(4\) (because the inequality includes equality, i.e., \(x = 4\) is a solution) and draw an arrow to the right (since \(x\) is greater than or equal to \(4\)).

Answer:

For \(x - 3\geq3\), the solution is \(x\geq6\) (closed circle at \(6\), arrow to the right).
For \(6\geq7 + x\), the solution is \(x\leq - 1\) (closed circle at \(-1\), arrow to the left).
For \(x + 8\geq5\), the solution is \(x\geq - 3\) (closed circle at \(-3\), arrow to the right).
For \(3\leq x + 10\), the solution is \(x\geq - 7\) (closed circle at \(-7\), arrow to the right).
For \(3\lt - 1+x\), the solution is \(x\gt4\) (open circle at \(4\), arrow to the right).
For \(x-10\lt - 4\), the solution is \(x\lt6\) (open circle at \(6\), arrow to the left).
For \(3 + x\lt3\), the solution is \(x\lt0\) (open circle at \(0\), arrow to the left).
For \(-5 + x\gt1\), the solution is \(x\gt6\) (open circle at \(6\), arrow to the right).
For \(-3\leq x-7\), the solution is \(x\geq4\) (closed circle at \(4\), arrow to the right).