Question

lesson 8.10
reteach
name
graph inequalities
you can graph the solutions of an inequality on a number line.

graph the inequality $n \geq 9$.
step 1 determine the meaning of the inequality.
$n \geq 9$ means \$n$ is greater than or equal to 9.\
step 2 draw a number line and circle the number given in the inequality.
step 3 decide whether to fill in the circle.
for $\leq$ or $\geq$, fill in the circle to show \or equal to.\ for $<$ or $>$, do not fill in the circle.
since the inequality uses $\geq$, 9 is a possible solution. so, fill in the circle.
step 4 shade from the circle in the direction of the remaining solutions.
since the inequality symbol is $\geq$, the shading covers all numbers greater than 9.

graph the inequality.

1. $k < 8$
2. $r \geq 6$
3. $w \leq 3$
4. $x > 3$

write the inequality shown by the graph.
5.
6.
r67
houghton mifflin harcourt publishing company

Explanation:

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Problems 1-4 (Graphing Inequalities)

1. $k < 8$

Step1: Interpret the inequality

$k < 8$ means "k less than 8"

Step2: Mark the value on number line

Circle the point $8$ on the number line (open circle, since $<$ means not equal to 8)

Step3: Shade the solution region

Shade all numbers left of 8 (values less than 8)

2. $r \geq 6$

Step1: Interpret the inequality

$r \geq 6$ means "r ≥ 6"

Step2: Mark the value on number line

Circle the point $6$ on the number line (filled circle, since $\geq$ means equal to 6 is allowed)

Step3: Shade the solution region

Shade all numbers right of 6 (values greater than or equal to 6)

3. $w \leq 3$

Step1: Interpret the inequality

$w \leq 3$ means "w ≤ 3"

Step2: Mark the value on number line

Circle the point $3$ on the number line (filled circle, since $\leq$ means equal to 3 is allowed)

Step3: Shade the solution region

Shade all numbers left of 3 (values less than or equal to 3)

4. $x > 3$

Step1: Interpret the inequality

$x > 3$ means "x greater than 3"

Step2: Mark the value on number line

Circle the point $3$ on the number line (open circle, since $>$ means not equal to 3)

Step3: Shade the solution region

Shade all numbers right of 3 (values greater than 3)

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Problems 5-6 (Writing Inequalities from Graphs)

5.

Step1: Identify key graph features

Filled circle at $7$, shading right

Step2: Write matching inequality

Filled circle = $\geq$, shading right = greater than

6.

Step1: Identify key graph features

Open circle at $5$, shading right

Step2: Write matching inequality

Open circle = $>$, shading right = greater than

Answer:

1. (Graph: Open circle at 8, shade left of 8)
2. (Graph: Filled circle at 6, shade right of 6)
3. (Graph: Filled circle at 3, shade left of 3)
4. (Graph: Open circle at 3, shade right of 3)
5. $x \geq 7$
6. $x > 5$