IXL - Graph solutions to absolute value inequalities (Algebra 2 practice)

Solve for

and graph the solution.

Click two endpoints to graph a line segment, an endpoint and an arrowhead to graph a ray, or two arrowheads to graph a line. To change endpoints from filled-in circles to empty circles, click on them.

ref_doc_title.

Learn with an example

question

Solve for

and graph the solution.

≤

key idea

The inequality

is equivalent to

and

–

which has a solution of

–

The inequality

is equivalent to

–

which has a solution of

–

solution

Look at the inequality.

≤

Since

can be either positive or negative, split the inequality into two cases.

First, solve the positive case.

≤

–

≤

Subtract 8 from both sides

≥

Rewrite the inequality so that

is on the left

–

Rewrite the inequality so that

is on the left

Next, solve the negative case.

≤

–

(

)

≤

Apply the distributive property

–

Apply the distributive property

≤

Add 8 to both sides

–

Add 8 to both sides

–

≥

Multiply both sides by

–

and reverse the direction of the inequality symbol

Multiply both sides by

–

and reverse the direction of the inequality symbol

≤

Rewrite the inequality so that

is on the left

–

Rewrite the inequality so that

is on the left

Now, see if the two inequalities can be combined into a single statement. Since there aren't any numbers that are both greater than or equal to

–

and less than or equal to

–

the two solutions cannot be combined. Instead, they must be joined with

or.

≤

–

≥

–

Finally, graph

≤

–

≥

–

This compound inequality is written as two inequalities joined with

or,

so the graph should look like two rays with those values as their endpoints. Make sure to fill in the endpoints to show that they are included.

Looking for more? Try this:

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Teacher tools

Work it out

Not feeling ready yet? These can help:

G.4Solve absolute value inequalities

C.1Graph inequalities

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