Worksheets · Algebra 2

Absolute value equations worksheet for Algebra 2

Algebra 2 absolute value equations are the ones that can trap you: the bars sit inside a bigger expression, or there is a variable on both sides, so one of the two answers can be fake. Isolate the bars, split into two cases, and check every answer in the original.

Also taught in Algebra 1, at its own level and with its own examples.

Not quite the one you need? Same words, different skill:

Select your difficulty

Pick more than one for a sheet that mixes them.

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Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Absolute Value Equations

Date Period

Solve each equation.

  1. Isolate the absolute value, then solve

    50=4 ⁣∣r+3∣+6
  2. −5=3 ⁣∣−v−9∣−11
  3. 17=∣y+6∣+7
  4. 6 ⁣∣−y−10∣+7=79
  5. 10=∣n−10∣+6
  6. 8=∣−v+8∣+1
  7. ∣n−9∣−9=−3
  8. − ⁣∣−b+8∣+5=4
  9. ∣−a−5∣+5=6
  10. ∣a+2∣−10=1

  1. Solve with the variable outside the bars, or bars on both sides

    ∣2x+4∣=x−2
  2. ∣x−6∣=2x−7
  3. ∣x+4∣=3x+4
  4. ∣2x∣=x−4
  5. ∣x−5∣=2x+6
  6. ∣2x−4∣=x−5
  7. ∣2x+5∣=3x
  8. ∣2x+6∣=x
  9. ∣2x+2∣=x+6
  10. ∣x−4∣=2x

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Absolute Value EquationsAnswer keyVersion 2

Date Period

Solve each equation.

  1. Isolate the absolute value, then solve

    50=4 ⁣∣r+3∣+6{−14,8}
  2. −5=3 ⁣∣−v−9∣−11{−11,−7}
  3. 17=∣y+6∣+7{−16,4}
  4. 6 ⁣∣−y−10∣+7=79{−22,2}
  5. 10=∣n−10∣+6{6,14}
  6. 8=∣−v+8∣+1{1,15}
  7. ∣n−9∣−9=−3{3,15}
  8. − ⁣∣−b+8∣+5=4{7,9}
  9. ∣−a−5∣+5=6{−6,−4}
  10. ∣a+2∣−10=1{−13,9}

  1. Solve with the variable outside the bars, or bars on both sides

    ∣2x+4∣=x−2No solution
  2. ∣x−6∣=2x−7{133}
  3. ∣x+4∣=3x+4{0}
  4. ∣2x∣=x−4No solution
  5. ∣x−5∣=2x+6{−13}
  6. ∣2x−4∣=x−5No solution
  7. ∣2x+5∣=3x{5}
  8. ∣2x+6∣=xNo solution
  9. ∣2x+2∣=x+6{−83,4}
  10. ∣x−4∣=2x{43}

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

How to do these

∣x−3∣=2x

  1. Case one: x - 3 = 2x gives x = -3.
  2. Case two: x - 3 = -2x gives x = 1.
  3. Check: x = -3 makes the right side -6, and an absolute value can never be negative, so reject it.

The answer is {1}.

Where students go wrong

Keeping both answers without checking. When x appears outside the bars, one case often gives a solution that makes the other side negative.

Also called modulus equations.

What you can put on this worksheet

A single absolute value
∣v−1∣=8 → {−7,9}
Mix in some with no solution
∣v+7∣=−1 → No solution
Numbers outside the bars on both sides
3 ⁣∣v+1∣−7=2 → {−4,2}
The variable outside the bars too
∣x∣=2x+2 → {−23}
Fractions inside or outside, bars equal to zero
∣7k−5∣6=2 → {−1,177}

Questions about these worksheets

Yes. Every absolute value equations sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Algebra 2 is usually taken around 10th or 11th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the absolute value equations questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

You pick from 5: a single absolute value, mix in some with no solution, numbers outside the bars on both sides, the variable outside the bars too and fractions inside or outside, bars equal to zero. Tick as many as you want and set how many of each, or let it spread them evenly.

Solving only the positive case, which loses half the answers. The other one is dropping the bars too early: in 2|n - 5| + 1 = 9 you have to get the absolute value on its own first, so |n - 5| = 4, and only then split it.