Worksheets · Algebra 1

Absolute value equations worksheet for Algebra 1

An absolute value equation splits into two, and both have to be solved. When the variable is outside the bars as well, each answer has to be checked, and some fail, leaving one solution or none. You can also mix in equations equal to a negative, which have no solution at all and are the fastest way to find out whether students are reading or just following steps.

Also taught in Algebra 2, at its own level and with its own examples.

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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

    6 ⁣∣−a−5∣=54
  2. ∣p+6∣=1
  3. 9=∣3r−15∣
  4. − ⁣∣v−8∣=−4
  5. 3=∣−r+10∣
  6. ∣5b+40∣=15
  7. − ⁣∣a+6∣=−3
  8. 21=3 ⁣∣b−3∣
  9. ∣−y−2∣=3
  10. 39=∣3y+15∣

  1. Solve with the variable outside the bars

    ∣x−5∣=2x−5
  2. ∣x+2∣=2x+3
  3. ∣2x−1∣=x−6
  4. ∣2x+5∣=x+5
  5. ∣x−2∣=3x+4
  6. ∣2x+3∣=x−4
  7. ∣x+1∣=2x−5
  8. ∣x−4∣=2x
  9. ∣x∣=2x−3
  10. ∣2x−2∣=3x+2

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

Sigma Prep · sigmaprep.io/worksheets

Name

Absolute Value EquationsAnswer keyVersion 1

Date Period

Solve each equation.

  1. Isolate the absolute value, then solve

    6 ⁣∣−a−5∣=54{−14,4}
  2. ∣p+6∣=1{−7,−5}
  3. 9=∣3r−15∣{2,8}
  4. − ⁣∣v−8∣=−4{4,12}
  5. 3=∣−r+10∣{7,13}
  6. ∣5b+40∣=15{−11,−5}
  7. − ⁣∣a+6∣=−3{−9,−3}
  8. 21=3 ⁣∣b−3∣{−4,10}
  9. ∣−y−2∣=3{−5,1}
  10. 39=∣3y+15∣{−18,8}

  1. Solve with the variable outside the bars

    ∣x−5∣=2x−5{103}
  2. ∣x+2∣=2x+3{−1}
  3. ∣2x−1∣=x−6No solution
  4. ∣2x+5∣=x+5{−103,0}
  5. ∣x−2∣=3x+4{−12}
  6. ∣2x+3∣=x−4No solution
  7. ∣x+1∣=2x−5{6}
  8. ∣x−4∣=2x{43}
  9. ∣x∣=2x−3{3}
  10. ∣2x−2∣=3x+2{0}

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

How to do these

∣x+3∣=7

  1. Whatever is inside is 7 units from zero, either way.
  2. So x + 3 = 7 or x + 3 = -7.
  3. Solve both.

The answer is {4,−10}.

Where students go wrong

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.

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 1 is usually taken around 8th or 9th 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.