Solving Linear Equations Examples in Math
Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Solving Linear Equations.
This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.
Concept Recap
The process of finding the value of the variable that makes a linear equation true, using inverse operations to isolate the variable on one side of the equals sign. A linear equation has the variable raised only to the first power, producing exactly one solution.
Undo what's done to x by doing the opposite: if x + 5, subtract 5.
Read the full concept explanation →How to Use These Examples
- Read the first worked example with the solution open so the structure is clear.
- Try the practice problems before revealing each solution.
- Use the related concepts and background knowledge badges if you feel stuck.
What to Focus On
Core idea: Inverse operations (+ - \times \div) undo each other to isolate the variable.
Common stuck point: Order matters—undo addition/subtraction before multiplication/division.
Sense of Study hint: Write each inverse operation step on its own line, applying it to both sides before moving on.
Worked Examples
Example 1
easySolution
- 1 Subtract 7 from both sides: 3x = 22 - 7 = 15.
- 2 Divide both sides by 3: x = \frac{15}{3} = 5.
- 3 Check: 3(5) + 7 = 15 + 7 = 22 ✓
Answer
Example 2
mediumExample 3
mediumPractice Problems
Try these problems on your own first, then open the solution to compare your method.
Example 1
easyExample 2
hardRelated Concepts
Background Knowledge
These ideas may be useful before you work through the harder examples.