Question

review sheet: inequalities
draw a graph for each inequality.

1. $-v \leq -3$

2)

1. $m \geq -6$
2. $k \geq -3$
3. $x > 0$

write an inequality for each graph.
6)
7)
8)
9)
10)
solve each inequality and graph its solution.

1. $-2x > 18$
2. $13 - p > 2$
3. $\frac{m}{9} < -19$
4. $300 \geq -20n$
5. $14 \leq x + 17$

$20 < \frac{r}{12}$

Explanation:

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Part 1: Graph each inequality

Step1: Solve inequality 1

Multiply by -1 (reverse sign):
$-v \leq -3 \implies v \geq 3$

• Graph: Closed dot at 3, shade right.

Step2: Graph inequality 2

$x > 4$

• Graph: Open dot at 4, shade right.

Step3: Graph inequality 3

$m \geq -6$

• Graph: Closed dot at -6, shade right.

Step4: Graph inequality 4

$k \geq -3$

• Graph: Closed dot at -3, shade right.

Step5: Graph inequality 5

$x > 0$

• Graph: Open dot at 0, shade right.

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Part 2: Write inequality for each graph

Step6: Analyze graph 6

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

Step7: Analyze graph7

Open dot at -4, shade right:
$x > -4$

Step8: Analyze graph8

Open dot at 6, shade right:
$x > 6$

Step9: Analyze graph9

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

Step10: Analyze graph10

Closed dot at 1, shade left:
$x \leq 1$

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Part3: Solve and graph inequalities

Step11: Solve inequality11

Divide by -2 (reverse sign):
$-2x > 18 \implies x < -9$

• Graph: Open dot at -9, shade left.

Step12: Solve inequality12

Subtract 13, multiply by -1:
$13-p > 2 \implies -p > -11 \implies p < 11$

• Graph: Open dot at 11, shade left.

Step13: Solve inequality13

Multiply by 9:
$\frac{m}{9} < -19 \implies m < -171$

• Graph: Open dot at -171, shade left.

Step14: Solve inequality14

Divide by -20 (reverse sign):
$300 \geq -20n \implies -15 \leq n \implies n \geq -15$

• Graph: Closed dot at -15, shade right.

Step15: Solve inequality15

Multiply by 12:
$20 < \frac{r}{12} \implies r > 240$

• Graph: Open dot at 240, shade right.

Step16: Solve inequality16

Subtract 17:
$14 \leq x+17 \implies x \geq -3$

• Graph: Closed dot at -3, shade right.

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Answer:

Part 1 (Graphs):

1. Closed dot at 3, shade right
2. Open dot at 4, shade right
3. Closed dot at -6, shade right
4. Closed dot at -3, shade right
5. Open dot at 0, shade right

Part 2 (Inequalities from Graphs):

1. $x \leq -1$
2. $x > -4$
3. $x > 6$
4. $x \geq 3$
5. $x \leq 1$

Part 3 (Solved Inequalities + Graphs):

1. $x < -9$; Open dot at -9, shade left
2. $p < 11$; Open dot at 11, shade left
3. $m < -171$; Open dot at -171, shade left
4. $n \geq -15$; Closed dot at -15, shade right
5. $r > 240$; Open dot at 240, shade right
6. $x \geq -3$; Closed dot at -3, shade right