Two-step equations: printable worksheets
Solve px + q = r, x/p + q = r, q - px = r and p(x + q) = r, with worked steps and a check.
Sample worksheet
The first 6 problems of a real worksheet, made the way the builder makes it. Open it in the builder to change the number of problems, the difficulty and the layout, then print.
Show answers
A two-step equation is the first kind of algebra problem where one move is not enough. To find the unknown number, a student has to undo what was done to it in the opposite order: first the adding or subtracting, then the multiplying or dividing. Learning to do that calmly, and to check the answer by putting it back into the equation, is one of the most useful habits in seventh grade math.
This worksheet creates equations in four common shapes. Some multiply the variable and then add a number, some divide the variable and then add, some subtract the variable term from a number, and some multiply a whole bracketed sum. You can limit the practice to the first two shapes for a gentle start, or ask for all four. Coefficients can stay as whole numbers, or you can bring in fractions and decimals for a real challenge. You can also allow negative numbers, pick the letter used for the variable, and require that every solution is a whole number so that the arithmetic stays clean.
Getting the most from it
Each answer key can show the worked steps and a check, so a student who is stuck can compare their own working with a model. Encourage them to write each step on its own line and to do the same thing to both sides.
- Begin with positive numbers and the letter x, then add negatives.
- Mix the variable letters to show that the letter does not change the method.
- Turn on the distribute first option to practice opening a bracket before solving.
Use the button above to open this sample in the builder, then change the settings and print your own sheet.
What students practise
I can solve two-step equations and check my answer.
Students solve two-step linear equations with inverse operations in reverse order and check the solution by substitution.
Key words
- variable
- a letter that stands for an unknown number
- inverse operation
- an operation that undoes another
- solution
- the value that makes the equation true
Common mistakes
- Applies an operation to only one side.
- Divides before undoing the constant term.
- Drops a negative sign when undoing subtraction.
Standards
Common Core State Standards this worksheet practises.
- 7.EE.B.4a: Solve word problems leading to equations of the form px + q = r and p(x + q) = r. (unverified)
Related topics
- Before this: Properties of multiplication (Grade 3)
- Next: Factoring trinomials (Algebra 1)