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Linear Equations

A free College Algebra lesson from the “Linear Equations and Inequalities” unit, with a worked example and practice problems including step-by-step solutions.

Linear equations can be solved by simplifying both sides, collecting variable terms on one side, and using inverse operations to isolate the variable.

What you'll learn

Why it matters: Budgets, dosage formulas, pricing plans, and unit-conversion equations all depend on isolating one unknown without changing the relationship. The trustworthy habit is to undo operations in order and check the result back in the original situation.

Worked example

Problem. Solve 4x - 7 = 21.

  1. Add 7 to both sides: 4x = 28.
  2. Divide by 4.
  3. x = 7.

Answer: 7

Lesson preview: this page shows 5 practice items. The interactive activity contains 28 practice items and 15 quiz items (typed response and multiple choice). Counts include repeated prompts and variants.

Practice problems

1. Solve 3x + 8 = 29.

Show solution
  1. Subtract 8, then divide by 3.

Answer: 7

2. Solve 5x - 11 = 34.

Show solution
  1. Add 11, then divide by 5.

Answer: 9

3. Solve 2(x - 4) = 18.

Show solution
  1. Divide by 2, then add 4.

Answer: 13

4. Solve 7x - 13 = 43.

Show solution
  1. Add 13, then divide by 7.

Answer: 8

5. Solve 4(x + 3) - 5 = 31.

Show solution
  1. Distribute or simplify inside first, then isolate x.

Answer: 6

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