IXL - Graph solutions to absolute value inequalities (Algebra 1 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.

≥

–

≥

Add 2 to 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

–

≥

Subtract 2 from both sides

–

Subtract 2 from 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. The variable

is less than or equal to 3 and greater than or equal to 1, which means it is between the two values. Write the solution as a single statement.

≤

Finally, graph

≤

This compound inequality is written with the variable between two values, so the graph should look like a line segment with those two values as its endpoints. Make sure to fill in the endpoints to show that they are included.

Looking for more? Try these:

Lesson: Absolute value inequalities

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Teacher tools

Work it out

Not feeling ready yet? These can help:

F.15Graph solutions to compound inequalities

H.4Solve absolute value inequalities

Lesson: Absolute value inequalities

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