Question

for questions 13 - 18, draw a graph for each inequality.

1. (bleq - 2)
2. (ngeq0)
3. (v > - 1)
4. (n < 4)
5. (a>3)
6. (pleq3)

for questions 19 - 24, write an inequality for each graph.
19.
20.
21.
22.
23.
24.

Explanation:

Step1: Graphing inequalities with $\leq$ or $\geq$

For inequalities like $b\leq - 2$ and $n\geq0$ and $p\leq3$, we use a closed - circle on the number on the number line (because the number is included in the solution set) and draw an arrow in the appropriate direction. For $b\leq - 2$, we put a closed - circle at $-2$ and draw an arrow to the left. For $n\geq0$, we put a closed - circle at $0$ and draw an arrow to the right. For $p\leq3$, we put a closed - circle at $3$ and draw an arrow to the left.

Step2: Graphing inequalities with $>$ or $<$

For inequalities like $v > - 1$, $n < 4$ and $a>3$, we use an open - circle on the number on the number line (because the number is not included in the solution set) and draw an arrow in the appropriate direction. For $v > - 1$, we put an open - circle at $-1$ and draw an arrow to the right. For $n < 4$, we put an open - circle at $4$ and draw an arrow to the left. For $a>3$, we put an open - circle at $3$ and draw an arrow to the right.

Step3: Writing inequalities from graphs

If the graph has a closed - circle at a number $x$ and an arrow to the left, the inequality is $y\leq x$. If it has a closed - circle at $x$ and an arrow to the right, the inequality is $y\geq x$. If it has an open - circle at $x$ and an arrow to the left, the inequality is $y < x$. If it has an open - circle at $x$ and an arrow to the right, the inequality is $y>x$.

1. On a number line, put a closed - circle at $-2$ and draw an arrow to the left.
2. On a number line, put a closed - circle at $0$ and draw an arrow to the right.
3. On a number line, put an open - circle at $-1$ and draw an arrow to the right.
4. On a number line, put an open - circle at $4$ and draw an arrow to the left.
5. On a number line, put an open - circle at $3$ and draw an arrow to the right.
6. On a number line, put a closed - circle at $3$ and draw an arrow to the left.

19 - 24: Without seeing the actual graphs, the general process is as described above.

Answer:

1. Graph: Closed - circle at $-2$, arrow to the left.
2. Graph: Closed - circle at $0$, arrow to the right.
3. Graph: Open - circle at $-1$, arrow to the right.
4. Graph: Open - circle at $4$, arrow to the left.
5. Graph: Open - circle at $3$, arrow to the right.
6. Graph: Closed - circle at $3$, arrow to the left.

19 - 24: Answers depend on the specific graphs.