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

Using inverse operations in reverse order to isolate the variable and find its exact numerical value.

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

easy
Solve 3x + 7 = 22.

Solution

  1. 1
    Subtract 7 from both sides: 3x = 22 - 7 = 15.
  2. 2
    Divide both sides by 3: x = \frac{15}{3} = 5.
  3. 3
    Check: 3(5) + 7 = 15 + 7 = 22 ✓

Answer

x = 5
To solve a linear equation, isolate x by performing inverse operations. Always verify your answer by substituting back into the original equation.

Example 2

medium
Solve 2(x - 3) + 4 = 3x - 8.

Example 3

medium
Solve 2(3x - 4) = 5x + 6.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy
Solve 5x - 3 = 12.

Example 2

hard
Solve \frac{2x + 1}{3} = \frac{x - 2}{2}.
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Background Knowledge

These ideas may be useful before you work through the harder examples.

equationsorder of operations