IXL - Solve absolute value inequalities (Algebra 1 practice)

Solve for

–

≥

Write a compound inequality like 1 < x < 3 or like x < 1 or x >

Use integers, proper fractions, or improper fractions in simplest form.

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question

Solve for

Write a compound inequality like 1 < x < 3 or like x < 1 or x >

Use integers, proper fractions, or improper fractions in simplest form.

key idea

≥

then

is equivalent to

–

and

which has a solution of

–

≥

then

is equivalent to

–

which has a solution of

–

solution

Look at the inequality.

This inequality is equivalent to:

and

–

Solve the first inequality.

Divide both sides by 2

Solve the second inequality.

–

Divide both sides by

–

and reverse the direction of the inequality symbol

–

Divide both sides by

–

and reverse the direction of the inequality symbol

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

–

and greater than 2, the two solutions cannot be combined. Instead, they must be joined with

or.

–

Looking for more? Try these:

Lesson: Absolute value inequalities

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Work it out

Not feeling ready yet? These can help:

F.14Solve compound inequalities

H.1Solve absolute value equations

Lesson: Absolute value inequalities

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