Multi-Step Equations Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Multi-Step 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

Solving equations that require more than one inverse operation—typically involving distributing, combining like terms, and moving variables to one side before isolating the variable.

A one-step equation is like unwrapping one layer of packaging. A multi-step equation has several layers: first simplify each side (distribute, combine like terms), then peel off operations one at a time until x stands alone. Think of it as cleaning up a messy room before finding what you're looking for.

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: Simplify each side first (distribute and combine like terms), then use inverse operations to isolate the variable. If variables appear on both sides, collect them on one side first.

Common stuck point: When variables appear on both sides like 5x + 3 = 2x + 15, subtract the smaller variable term from both sides first: 3x + 3 = 15, then solve.

Sense of Study hint: Simplify each side separately first (distribute and combine like terms), then move variables to one side.

Worked Examples

Example 1

easy
Solve 3(x + 2) - 4 = 14.

Solution

  1. 1
    Distribute: 3x + 6 - 4 = 14.
  2. 2
    Simplify: 3x + 2 = 14.
  3. 3
    Subtract 2: 3x = 12.
  4. 4
    Divide by 3: x = 4.

Answer

x = 4
Multi-step equations require multiple inverse operations. Distribute first, then combine like terms, then isolate the variable.

Example 2

medium
Solve \frac{x+1}{2} - \frac{x-3}{4} = 3.

Practice Problems

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

Example 1

easy
Solve 2(x - 5) = 8.

Example 2

hard
Solve 5 - 2(3x + 1) = 4x - 7.

Background Knowledge

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

solving linear equationsdistributive propertyexpressions