Question

graphing inequalities
graph the inequality:

1. x≥ - 2
2. x < 5
3. x≤6
4. x > 1
5. x < - 14
6. x≤9
7. x > - 2
8. x≥ - 15
9. x≤ - 10
10. x > 16
11. x > - 1
12. x≥ - 3

Explanation:

Step1: Identify inequality type

For $x\geq - 2$, mark - 2 with a closed circle (because of $\geq$) and shade to the right.

Step2: For $x < 5$

Mark 5 with an open circle (because of $<$) and shade to the left.

Step3: For $x\leq6$

Mark 6 with a closed circle and shade to the left.

Step4: For $x > 1$

Mark 1 with an open circle and shade to the right.

Step5: For $x < - 14$

Mark - 14 with an open circle and shade to the left.

Step6: For $x\leq9$

Mark 9 with a closed circle and shade to the left.

Step7: For $x > - 2$

Mark - 2 with an open circle and shade to the right.

Step8: For $x\geq - 15$

Mark - 15 with a closed circle and shade to the right.

Step9: For $x\leq - 10$

Mark - 10 with a closed circle and shade to the left.

Step10: For $x > 16$

Mark 16 with an open circle and shade to the right.

Step11: For $x > - 1$

Mark - 1 with an open circle and shade to the right.

Step12: For $x\geq - 3$

Mark - 3 with a closed circle and shade to the right.

Answer:

The graphs are as follows:

1. For $x\geq - 2$, a closed - circle at - 2 and shading to the right on the number line.
2. For $x < 5$, an open - circle at 5 and shading to the left on the number line.
3. For $x\leq6$, a closed - circle at 6 and shading to the left on the number line.
4. For $x > 1$, an open - circle at 1 and shading to the right on the number line.
5. For $x < - 14$, an open - circle at - 14 and shading to the left on the number line.
6. For $x\leq9$, a closed - circle at 9 and shading to the left on the number line.
7. For $x > - 2$, an open - circle at - 2 and shading to the right on the number line.
8. For $x\geq - 15$, a closed - circle at - 15 and shading to the right on the number line.
9. For $x\leq - 10$, a closed - circle at - 10 and shading to the left on the number line.
10. For $x > 16$, an open - circle at 16 and shading to the right on the number line.
11. For $x > - 1$, an open - circle at - 1 and shading to the right on the number line.
12. For $x\geq - 3$, a closed - circle at - 3 and shading to the right on the number line.