Question

graph the inequality:

1. ( xgeq - 2 )
2. ( x < 5 )
3. ( xleq 6 )
4. ( x > 1 )
5. ( x < - 14 )
6. ( xleq 9 )
7. ( x > - 2 )
8. ( xgeq - 15 )
9. ( xleq - 10 )
10. ( x > 16 )
11. ( x > - 1 )
12. ( xgeq - 3 )

Explanation:

Step1: Graphing $x\geq - 2$

For the inequality \(x\geq - 2\), we use a closed circle at \(-2\) (because the inequality includes equality) and shade to the right (since \(x\) is greater than or equal to \(-2\)).

Step2: Graphing \(x < 5\)

For the inequality \(x < 5\), we use an open circle at \(5\) (because the inequality does not include equality) and shade to the left (since \(x\) is less than \(5\)).

Step3: Graphing \(x\leq 6\)

For the inequality \(x\leq 6\), we use a closed circle at \(6\) (because the inequality includes equality) and shade to the left (since \(x\) is less than or equal to \(6\)).

Step4: Graphing \(x > 1\)

For the inequality \(x > 1\), we use an open circle at \(1\) (because the inequality does not include equality) and shade to the right (since \(x\) is greater than \(1\)).

Step5: Graphing \(x < - 14\)

For the inequality \(x < - 14\), we use an open circle at \(-14\) (because the inequality does not include equality) and shade to the left (since \(x\) is less than \(-14\)).

Step6: Graphing \(x\leq 9\)

For the inequality \(x\leq 9\), we use a closed circle at \(9\) (because the inequality includes equality) and shade to the left (since \(x\) is less than or equal to \(9\)).

Step7: Graphing \(x > - 2\)

For the inequality \(x > - 2\), we use an open circle at \(-2\) (because the inequality does not include equality) and shade to the right (since \(x\) is greater than \(-2\)).

Step8: Graphing \(x\geq - 15\)

For the inequality \(x\geq - 15\), we use a closed circle at \(-15\) (because the inequality includes equality) and shade to the right (since \(x\) is greater than or equal to \(-15\)).

Step9: Graphing \(x\leq - 10\)

For the inequality \(x\leq - 10\), we use a closed circle at \(-10\) (because the inequality includes equality) and shade to the left (since \(x\) is less than or equal to \(-10\)).

Step10: Graphing \(x > 16\)

For the inequality \(x > 16\), we use an open circle at \(16\) (because the inequality does not include equality) and shade to the right (since \(x\) is greater than \(16\)).

Step11: Graphing \(x > - 1\)

For the inequality \(x > - 1\), we use an open circle at \(-1\) (because the inequality does not include equality) and shade to the right (since \(x\) is greater than \(-1\)).

Step12: Graphing \(x\geq - 3\)

For the inequality \(x\geq - 3\), we use a closed circle at \(-3\) (because the inequality includes equality) and shade to the right (since \(x\) is greater than or equal to \(-3\)).

Answer:

1. Closed circle at \(-2\), shade right.
2. Open circle at \(5\), shade left.
3. Closed circle at \(6\), shade left.
4. Open circle at \(1\), shade right.
5. Open circle at \(-14\), shade left.
6. Closed circle at \(9\), shade left.
7. Open circle at \(-2\), shade right.
8. Closed circle at \(-15\), shade right.
9. Closed circle at \(-10\), shade left.
10. Open circle at \(16\), shade right.
11. Open circle at \(-1\), shade right.
12. Closed circle at \(-3\), shade right.