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
- Solve multi-step linear equations
- Use inverse operations
- Check solutions in context
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.
- Add 7 to both sides: 4x = 28.
- Divide by 4.
- x = 7.
Answer: 7
Practice problems
1. Solve 3x + 8 = 29.
Show solution
- Warm-up: First identify exactly what the question is asking: Solve 3x + 8 = 29.
- Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
- Subtract 8, then divide by 3.
- Check the result by substituting or estimating: the response should match 7 and make sense in the original problem.
Answer: 7
2. Solve 5x - 11 = 34.
Show solution
- Core Practice: First identify exactly what the question is asking: Solve 5x - 11 = 34.
- Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
- Add 11, then divide by 5.
- Check the result by substituting or estimating: the response should match 9 and make sense in the original problem.
Answer: 9
3. Solve 2(x - 4) = 18.
Show solution
- Challenge: First identify exactly what the question is asking: Solve 2(x - 4) = 18.
- Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
- Divide by 2, then add 4.
- Check the result by substituting or estimating: the response should match 13 and make sense in the original problem.
Answer: 13
4. Solve 7x - 13 = 43.
Show solution
- Core Practice: First identify exactly what the question is asking: Solve 7x - 13 = 43.
- Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
- Add 13, then divide by 7.
- Check the result by substituting or estimating: the response should match 8 and make sense in the original problem.
Answer: 8
5. Solve 4(x + 3) - 5 = 31.
Show solution
- Core Practice: First identify exactly what the question is asking: Solve 4(x + 3) - 5 = 31.
- Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
- Distribute or simplify inside first, then isolate x.
- Check the result by substituting or estimating: the response should match 6 and make sense in the original problem.
Answer: 6
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