Multi step equations worksheets give students practice with equations that take more than two steps: distributing, combining like terms and moving variables from one side to the other. These free printable worksheets build from a(x + b) = c up to equations with parentheses and variables on both sides. Every PDF has an answer key, and the maker below creates new problems on demand.
Quick answer: To solve a multi-step equation, distribute, combine like terms, move the variable terms to one side, then undo addition or subtraction and finally multiplication or division. For 3(x + 4) = 27, distribute to get 3x + 12 = 27, subtract 12, and divide by 3 to get x = 5. This page has 7 free multi step equations worksheets (PDF) with answer keys, plus a maker. Updated October 2026.
Ready-to-print samples
A few of the ready PDFs on this page. The full list is under Ready-to-print worksheets, and the maker above makes new problems on demand.
Distribute: a(x + b) = cLevel 1 with a full answer key.PDFCombine like termsLevel 2 with a full answer key.PDFVariables on both sidesLevel 3 with a full answer key.PDFParentheses and variables on both sidesLevel 4 with a full answer key.PDF
How to solve multi-step equations
Distribute any number outside parentheses to every term inside.
Combine like terms on each side of the equals sign.
Move the variable terms to one side by adding or subtracting the same term from both sides.
Undo addition or subtraction, then undo multiplication or division.
Check by substituting the answer into the original equation.
Distributive property equations worksheet: worked examples
When a number multiplies a bracket, distribute it first. Each row shows the equation after distributing and the solution:
Equation
Distribute
Isolate the x term
Solution
3(x + 4) = 27
3x + 12 = 27
3x = 15
x = 5
2(x − 3) = 8
2x − 6 = 8
2x = 14
x = 7
4(x + 1) = -4
4x + 4 = -4
4x = -8
x = -2
5(x + 2) = 25
5x + 10 = 25
5x = 15
x = 3
Combining like terms equations worksheet
Like terms have the same variable part, so 3x and 2x combine to 5x. Combine first, then solve as a two-step equation:
Equation
Combine like terms
Then solve
Solution
3x + 2x + 4 = 29
5x + 4 = 29
5x = 25
x = 5
7x − 3x + 6 = 22
4x + 6 = 22
4x = 16
x = 4
x + 5 + 2x − 8 = 18
3x − 3 = 18
3x = 21
x = 7
9x − 4x − 2 = 13
5x − 2 = 13
5x = 15
x = 3
Equations with variables on both sides worksheet
Subtract the smaller variable term from both sides so that x appears on one side only. Check by substituting the answer back into both sides:
Equation
Collect x on one side
Solution
Check
5x + 3 = 2x + 12
3x = 9
x = 3
Check: 18 = 18
7x − 4 = 3x + 8
4x = 12
x = 3
Check: 17 = 17
4x + 9 = 6x + 1
-2x = -8
x = 4
Check: 25 = 25
9x + 2 = 4x − 13
5x = -15
x = -3
Check: -25 = -25
Try ten multi-step equations
Use these as a warm-up. Show every step on paper, then substitute your answer to check.
#
Problem
Answer
1
3(x + 2) = 21
x = 5
2
5x + 4 = 2x + 19
x = 5
3
4x − 7 = 2x + 9
x = 8
4
2(3x − 1) = 22
x = 4
5
6x + 2x − 5 = 27
x = 4
6
9 − 2x = 3x − 1
x = 2
7
-(x + 3) = 8
x = -11
8
3(x − 4) + 6 = 15
x = 7
9
7x + 3 = 5x − 9
x = -6
10
2(x + 5) = 4x − 6
x = 8
Solving multi step equations worksheet and multi step equations practice
A solving multi step equations worksheet works best when students write one step per line and keep the equals signs lined up. The multi step equations worksheets on this page leave space for that working. For extra multi step equations practice, print a fresh set from the maker, solve it, and use the answer key to find the first line where an error crept in.
Good multi step equations practice also includes checking. Substituting the answer back into the original equation takes a minute and catches almost every sign error. Many teachers set a rule that the multi step equations worksheets are not finished until every answer has a check beside it.
How to use these multi step equations worksheets
Use the multi step equations worksheets in order. Start with the distribute sheets so that students master the distributive property, then move to combining like terms, and finish with variables on both sides. Every one of the multi step equations worksheets has an answer key on the last page, so students can check their own work, and a weekly set is a good source of quick retests.
Once the five steps are automatic, mix the problem types for review. Print a multi step equations worksheet for homework and review it together the next day. Students who need more multi step equations worksheets can generate a new set in the maker, and multi step equations worksheets with fresh numbers make a reliable weekly check.
Multi-step equations vocabulary
Students answer questions faster when they know the words. These are the terms used on the worksheets and answer keys:
Word
Meaning
Example
Variable
A letter that stands for an unknown number
x
Like terms
Terms with the same variable part
3x and 5x
Distributive property
a(b + c) = ab + ac
3(x + 4) = 3x + 12
Inverse operation
The operation that undoes another
Subtraction undoes addition
Coefficient
The number multiplying a variable
5 in 5x
Solution
The value of the variable that makes the equation true
Solve word problems leading to equations of the form px + q = r and p(x + q) = r
Grade 8
8.EE.C.7
Solve linear equations in one variable, including variables on both sides and parentheses
Grade 8
8.EE.C.7b
Solve equations that need the distributive property and combining like terms
Common mistakes with multi-step equations
Mistake
Example
Fix
Distributing to the first term only
3(x + 4) = 3x + 4
Multiply every term inside: 3x + 12
Sign error when distributing
2(x − 5) = 2x − 5
Multiply the sign too: 2x − 10
Moving a term without changing its sign
5x + 3 = 2x + 12 so 5x + 2x = 12 + 3
Subtract 2x from both sides: 3x + 3 = 12
Dividing only part of the equation
4x = 20 + 8, so x = 5 + 8
Divide every term: x = 7
Skipping the check
Not substituting x back in
Substitute the answer to see that both sides match
Real-life uses of multi-step equations
Many everyday problems need more than two steps:
Situation
Equation
Answer
Two gyms: $20 plus $5 a visit, or $8 a visit. When are costs equal?
20 + 5x = 8x
x = 6.67, so 7 visits
A rectangle has perimeter 54 and length x + 5 and width x
2(x + 5) + 2x = 54
x = 11
A phone plan costs $15 plus $2 for each of 3 extra services, total $27
15 + 3(2x) = 27
x = 2
Three friends buy the same shirt and share a $6 coupon, paying $42 in all
3(x − 2) = 42
x = 16
Two plants grow at different rates, one 5 cm tall growing 3 cm a week, the other 9 cm growing 2 cm a week
5 + 3x = 9 + 2x
x = 4 weeks
Which multi step equations worksheet should you start with?
Students who can solve two-step equations can begin at level 1. Move to level 3 once distributing and combining are automatic. Set B gives a retest for the first three levels.
Level
Skill
Best for
Level 1
Distribute: a(x + b) = c
Grades 7 and 8
Level 2
Combine like terms
Grades 7 and 8
Level 3
Variables on both sides
Grade 8
Level 4
Parentheses and variables on both sides
Grade 8, extension
A weekly plan for multi-step equations
Day
Focus
Suggested block
Monday
Distribute and solve
15 min
Tuesday
Combine like terms
15 min
Wednesday
Variables on both sides
15 min
Thursday
Mixed review and checking
15 min
Weekly total
Four short sessions
60 min
Frequently asked questions
5 quick answers
Where can I download free multi step equations worksheets?
Open any worksheet in the Ready-to-print list on this page, choose US Letter or A4, then print or save the PDF. They are free, with answer keys, and no account is needed.
How do you solve a multi-step equation?
Distribute, combine like terms, move the variable terms to one side, then undo addition or subtraction and finally multiplication or division.
How do you solve equations with variables on both sides?
Subtract the smaller variable term from both sides so the variable is on one side only, then solve as a two-step equation.
What if the variables cancel out?
If you get a true statement like 5 = 5, there are infinitely many solutions. If you get a false statement like 3 = 7, there is no solution.
What grade solves multi-step equations?
Grade 7 solves two-step equations with parentheses, and grade 8 solves equations with variables on both sides.
