Printable pre-algebra, algebra and geometry worksheets

Absolute Value Worksheets Generator

Make printable absolute value practice – from evaluating |−8| to solving absolute value equations and graphing inequalities – with an answer key.

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This free absolute value worksheet generator creates printable practice sheets in your web browser. You choose the problem types, difficulty and number of problems, and it builds a sheet with an answer key, ready to print or save as a PDF. It covers evaluating absolute value expressions, comparing absolute values, solving absolute value equations and inequalities, and writing absolute value word problems.

No sign-up is needed, and nothing is uploaded: the problems are made on your own device. Teachers can print several versions for different groups, and students can practise with new numbers each time. Your settings are remembered for your next visit. The generator also works on phones and tablets, though printing needs a printer or a Save as PDF option. Everything you make here is free to use in class or in products you sell, such as Teachers Pay Teachers resources, Etsy printables or KDP workbooks.

Absolute value worksheets example

How to use the Absolute Value Worksheet Generator

  1. Tick one or more boxes under Problem types. Evaluate absolute value expressions and Absolute value equations are ticked when the page opens. When several types are ticked, the problems are shared evenly between them and grouped by type, each group with its own one-line instruction.
  2. Pick a Difficulty: Easy, Medium or Hard.
  3. Choose the Number of problems: 6, 8, 10, 12, 15, 20, 24 or 30.
  4. Open More options to change the layout. Set Columns (Automatic, 1, 2 or 3) and Paper size (Letter or A4). Type a Worksheet title to print at the top, and tick Name and date line if students need to fill one in. The Answer key on a separate page box is ticked by default.
  5. Check the preview on the right, which shows the sheet as it will print. Press Show answers to display each answer under its problem on screen. Press it again to hide them.
  6. Press New worksheet for a fresh random set with the same settings. No problem repeats on one sheet.
  7. Press Print / Save as PDF to open the print dialog. Choose Save as PDF there to keep a file.

To share the exact same sheet, press Copy link. The link stores the problem set as a number, so anyone who opens it gets the same problems. A shared link uses its own settings rather than your saved ones.

What is absolute value?

Absolute value is the distance of a number from 0 on the number line, so it is never negative. For example, |−8| = 8, |5| = 5 and |0| = 0. Because distance has no direction, a number and its opposite always have the same absolute value.

The bars also work as grouping symbols, so you simplify what is inside them first. For example, |3 − 10| = |−7| = 7. Be careful with an expression like −|27 + (−26)|: the bars are worked out first (27 + (−26) = 1, so |1| = 1), and then the negative sign is applied, giving −1.

How do you solve absolute value equations?

To solve |ax + b| = c when c > 0, split it into two equations: ax + b = c and ax + b = −c. Solve each one. This gives two solutions, because the expression inside the bars can be c units from 0 in either direction.

Isolate the absolute value first when other terms are present. For 2|x − 3| + 4 = 10, subtract 4 and divide by 2 to get |x − 3| = 3. Then x − 3 = 3 gives x = 6, and x − 3 = −3 gives x = 0.

If c = 0, there is one solution, because the expression inside must equal 0. If c < 0, there is no solution, because an absolute value cannot be negative. Word problems use the same method. A thermostat set to 71° that is exactly 3° away gives |x − 71| = 3, so x = 68 or x = 74.

How do you graph an absolute value inequality?

Solve it like the equation to find the two boundary points, then decide whether the solution lies between them or outside them. For |x + 1| ≤ 5, the boundary points are x = −6 and x = 4, and “less than or equal” means between them: −6 ≤ x ≤ 4, drawn as a segment with two closed circles. For |x − 5| ≥ 2, the answer is x ≤ 3 or x ≥ 7, drawn as two rays pointing away from each other. The Absolute value inequalities type prints each problem with a blank number line, and the answer key draws the solution on it.

Sample problems from this generator

  1. |−11 + 10| Answer: 1
  2. |−4 − 7| Answer: 11
  3. |3m + 15| = 3 Answer: m = −6, m = −4
  4. |4x + 40| = 0 Answer: x = −10

Frequently asked questions

Is there an answer key?

Yes. The Answer key on a separate page box is ticked by default. When you print, the key starts on a new page after the worksheet and lists every problem number with its answer. Where an answer is a graph, the key draws it. To see answers on screen instead, press Show answers.

Why can an absolute value equation have no solution?

An absolute value is a distance, and a distance cannot be negative. If the expression is isolated and set equal to a negative number, such as |x| = −5, no value of x works. The generator’s instruction says “If there is no solution, say so,” so students need to recognise this case.

How do you solve absolute value inequalities?

For |x| < c, the solution is −c < x < c, a segment between two points. For |x| > c, the solution is x < −c or x > c, which are two rays pointing outward. Use open circles for < and > and closed circles for ≤ and ≥. For example, |x| ≥ 8 gives x ≤ −8 or x ≥ 8.

Does the worksheet include absolute value of integers?

Yes. Evaluate absolute value expressions includes problems with negative integers inside the bars, such as |−13| + |14| − |15| = 12. Compare absolute values asks students to write <, > or = between two expressions, such as |3| ___ −8, which is |3| > −8.

Can I make more than one version of the same sheet?

Yes. Each press of New worksheet makes different problems with the same settings, so you can print several versions for different desks. Use Copy link if you want to keep one particular set for later.

Can I use these absolute value worksheets for commercial use?

Yes. The worksheets and answer keys you generate are free for personal, classroom and commercial use, such as Teachers Pay Teachers products, Etsy listings or a printed workbook. You do not need to credit this site. You may not copy the generator itself and offer it as your own tool.