Question

date 02/2/26 period 3
draw a graph for each inequality.

1. ( x < -3 )
2. ( n geq 2 )
3. ( x > 2 )
4. ( n geq 1 )
5. ( x leq -4 )
6. ( m leq 5 )
7. ( x > 5 )
8. ( n < 2 )
9. ( k leq 1 )
10. ( x < -2 )
11. ( -3 geq x )
12. ( 6 geq x )
13. ( 6 < m )
14. ( 6 leq m )

write an inequality for each graph.
15)
16)
17)
18)
19)
20)
21)
22)

Explanation:

Step1: Graph $x < -3$

• Open circle at $-3$, shade left.

Step2: Graph $n \geq 2$

• Closed circle at $2$, shade right.

Step3: Graph $x > 2$

• Open circle at $2$, shade right.

Step4: Graph $n \geq 1$

• Closed circle at $1$, shade right.

Step5: Graph $x \leq -4$

• Closed circle at $-4$, shade left.

Step6: Graph $m \leq 5$

• Closed circle at $5$, shade left.

Step7: Graph $x > 5$

• Open circle at $5$, shade right.

Step8: Graph $n < 2$

• Open circle at $2$, shade left.

Step9: Graph $k \leq 1$

• Closed circle at $1$, shade left.

Step10: Graph $x < -2$

• Open circle at $-2$, shade left.

Step11: Rewrite $-3 \geq x$ as $x \leq -3$

• Closed circle at $-3$, shade left.

Step12: Rewrite $6 \geq x$ as $x \leq 6$

• Closed circle at $6$, shade left.

Step13: Rewrite $6 < n$ as $n > 6$

• Open circle at $6$, shade right.

Step14: Graph $6 \leq m$ (or $m \geq 6$)

• Closed circle at $6$, shade right.

Step15: Derive inequality for graph

Open circle at $5$, shade left: $m < 5$

Step16: Derive inequality for graph

Open circle at $-6$, shade right: $x > -6$

Step17: Derive inequality for graph

Closed circle at $-1$, shade left: $x \leq -1$

Step18: Derive inequality for graph

Closed circle at $3$, shade right: $x \geq 3$

Step19: Derive inequality for graph

Closed circle at $2$, shade right: $x \geq 2$

Step20: Derive inequality for graph

Open circle at $-2$, shade right: $x > -2$

Step21: Derive inequality for graph

Open circle at $2$, shade left: $x < 2$

Step22: Derive inequality for graph

Open circle at $-3$, shade right: $x > -3$

Answer:

1. Open circle at $-3$, shade all values left of $-3$
2. Closed circle at $2$, shade all values right of $2$
3. Open circle at $2$, shade all values right of $2$
4. Closed circle at $1$, shade all values right of $1$
5. Closed circle at $-4$, shade all values left of $-4$
6. Closed circle at $5$, shade all values left of $5$
7. Open circle at $5$, shade all values right of $5$
8. Open circle at $2$, shade all values left of $2$
9. Closed circle at $1$, shade all values left of $1$
10. Open circle at $-2$, shade all values left of $-2$
11. Closed circle at $-3$, shade all values left of $-3$
12. Closed circle at $6$, shade all values left of $6$
13. Open circle at $6$, shade all values right of $6$
14. Closed circle at $6$, shade all values right of $6$
15. $m < 5$
16. $x > -6$
17. $x \leq -1$
18. $x \geq 3$
19. $x \geq 2$
20. $x > -2$
21. $x < 2$
22. $x > -3$