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Free Algebra Worksheets: Equations and Inequalities

Printable-style algebra worksheets with answer keys, plus verified free sites for more equation practice.

These printable-style worksheets let you practice one-step equations, two-step equations, combining like terms, and simple inequalities, with a full answer key for each set. This page also links to current free algebra practice sites for more problems.

One-step equation worksheet

A one-step equation needs a single operation to solve, adding, subtracting, multiplying or dividing the same amount on both sides.

  1. x + 7 = 12
  2. x − 5 = 9
  3. 4x = 28
  4. x / 3 = 6
  5. x + 14 = 20
  6. 9x = 63

This set covers one-step equations with positive whole numbers only. It doesn’t cover negative solutions or fractional coefficients, which belong in a harder set once these feel easy.

Two-step equation worksheet

A two-step equation needs two operations to solve. Undo addition or subtraction first, then undo multiplication or division.

  1. 2x + 3 = 11
  2. 3x − 4 = 17
  3. 5x + 6 = 31
  4. x / 2 + 5 = 9
  5. 4x − 7 = 21
  6. 6x + 2 = 44

Worked example. Solve 2x + 3 = 11. Subtract 3 from both sides: 2x = 8. Divide both sides by 2: x = 4. Check it: 2(4) + 3 = 8 + 3 = 11, which matches.

This set covers two-step equations with one variable and whole-number solutions. It doesn’t cover equations with the variable on both sides, which needs an extra step to combine first.

Combining like terms worksheet

Like terms have the same variable raised to the same power. Combining them means adding or subtracting their coefficients while the variable stays the same.

  1. 3x + 5x
  2. 7x − 2x + 4
  3. 4x + 3 − x + 8
  4. 2x − 4x + 6 − 2
  5. 5x + 3 − 2x − 1

Worked example. Simplify 4x + 3 − x + 8. Group the x terms: 4x − x = 3x. Group the number terms: 3 + 8 = 11. The simplified expression is 3x + 11.

This set covers combining like terms with one variable. It doesn’t cover expressions with two different variables, like 3x + 2y, where x terms and y terms stay separate.

Simple inequality worksheet

An inequality compares two expressions using greater than, less than, or their “or equal to” versions, instead of an equals sign. You solve it the same way as an equation, but flip the inequality sign if you multiply or divide both sides by a negative number.

  1. x + 4 > 9
  2. 2x < 10
  3. x − 3 ≥ 5
  4. 3x + 1 ≤ 16
  5. x / 2 > 4

Worked example. Solve x + 4 > 9. Subtract 4 from both sides: x > 5. No negative multiplication or division happened, so the sign doesn’t flip. Every number greater than 5 is a solution.

This set covers inequalities solved with positive numbers only. It doesn’t cover inequalities that require multiplying or dividing by a negative number, which is the case where the flip rule matters most.

Answer key

Show answers and reasoning

One-step equations

  1. x + 7 = 12 → x = 5. Check: 5 + 7 = 12.
  2. x − 5 = 9 → x = 14. Check: 14 − 5 = 9.
  3. 4x = 28 → x = 7. Check: 4 x 7 = 28.
  4. x / 3 = 6 → x = 18. Check: 18 / 3 = 6.
  5. x + 14 = 20 → x = 6. Check: 6 + 14 = 20.
  6. 9x = 63 → x = 7. Check: 9 x 7 = 63.

Two-step equations

  1. 2x + 3 = 11 → x = 4. Check: 2(4) + 3 = 11.
  2. 3x − 4 = 17 → x = 7. Check: 3(7) − 4 = 17.
  3. 5x + 6 = 31 → x = 5. Check: 5(5) + 6 = 31.
  4. x / 2 + 5 = 9 → x = 8. Check: 8 / 2 + 5 = 9.
  5. 4x − 7 = 21 → x = 7. Check: 4(7) − 7 = 21.
  6. 6x + 2 = 44 → x = 7. Check: 6(7) + 2 = 44.

Combining like terms

  1. 3x + 5x = 8x.
  2. 7x − 2x + 4 = 5x + 4.
  3. 4x + 3 − x + 8 = 3x + 11.
  4. 2x − 4x + 6 − 2 = −2x + 4.
  5. 5x + 3 − 2x − 1 = 3x + 2.

Simple inequalities

  1. x + 4 > 9 → x > 5.
  2. 2x < 10 → x < 5.
  3. x − 3 ≥ 5 → x ≥ 8.
  4. 3x + 1 ≤ 16 → x ≤ 5.
  5. x / 2 > 4 → x > 8.

This section covers checking your own answers against a key. It doesn’t cover partial credit or showing work, which a teacher or parent should judge directly.

More free algebra practice sources

These sites were checked and confirmed live and free to use.

This lesson covers one-step and two-step equations, combining like terms, and simple inequalities at an introductory level. It doesn’t cover systems of equations, quadratics or graphing, which build on these skills later in algebra.

These worksheets work well alongside the step-by-step lessons on our algebra page, and the same balancing idea carries over from what you already know about fractions and equivalent values. For more topics, visit our math hub.

Sources