Multi-Step Equations Examples: 46 Problems with Answers

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: Distribute and combine like terms first, then undo operations one at a time until the variable is alone.

Common stuck point: The procedure for multi-step equations is the easy part; the trap is distributing only to the first term. Asking "Does isolating $x$ take more than one step — distributing, combining, or moving variables first?" first is what keeps a correct-looking calculation from being attached to the wrong concept.

Sense of Study hint: Ask: Does isolating $x$ take more than one step — distributing, combining, or moving variables first?

Worked Examples

Example 1

easy

Solve

3(x + 2) - 4 = 14

Answer

x = 4

First step

Distribute:

3x + 6 - 4 = 14

Full solution

2
Simplify: $3x + 2 = 14$ .
3
Subtract 2: $3x = 12$ .
4
Divide by 3: $x = 4$ .

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

Example 3

medium

Solve

4(x - 3) + 2x = 18

Example 4

medium

Solve

\frac{2x + 1}{3} = \frac{x - 2}{2}

Example 5

medium

Identify whether

3(x + 2) = 3x + 6

has one, no, or infinitely many solutions.

Example 6

hard

Solve

3(2x - 1) - 4(x + 2) = 5(x - 3) + 6

Example 7

hard

A rectangle has perimeter

44

cm. Its length is

4

more than twice its width. Find the dimensions.

Example 8

challenge

A father is three times his son's age. In

10

years, the father will be twice the son's age. Find their current ages.

Practice Problems

x

a x + b = c

(with

a \ne 0

), in terms of

a

b

c

Example 21

challenge

A number doubled, plus

7

, equals three times the number minus

2

-15

. Set up and solve.

Example 38

hard

Solve for

x

in terms of

a

and

b

a(x - b) = bx + a

← Back to Multi-Step Equations Formula Explained Practice Mode

Related Concepts

Solving Linear Equations Distributive Property Expressions Systems of Equations Inequalities

Background Knowledge

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

solving linear equationsdistributive propertyexpressions