7th Grade Math · Two-Step Equations
p(x + q) = r Worksheets
Free and printable, with a full answer key. Every worksheet is generated fresh, so you can hand a different version to every student.
Equations such as 4(x − 2) = 12, with a number multiplying a group.
Or start with a ready-made version:
How it works: a quick refresher
For the adult at the table. These are the rules the worksheet practices, followed by one problem worked from start to finish.
| Strategy | How it works |
|---|---|
| Undo in reverse order | In 3x + 5 = 20 the x was multiplied by 3, then 5 was added. Undo the adding first, then the multiplying. |
| Subtract, then divide | 3x + 5 = 20 → 3x = 15 → x = 5. |
| Two ways with brackets | 4(x − 2) = 12: divide by 4 to get x − 2 = 3, or distribute to get 4x − 8 = 12. Both give x = 5. |
| Mind the signs | Dividing by a negative changes the sign: −5y = −25 gives y = 5. |
| Check by substituting | 3(5) + 5 = 20, so x = 5 is right. |
Worked example
Solve −5y + 8 = −17.
- Subtract 8 from both sides: −5y = −25.
- Divide both sides by −5: y = 5.
- Check: −5(5) + 8 = −25 + 8 = −17.
Ready-made versions
Three fixed versions you can link to or share. Each is a PDF with its own answer key.
- p(x + q) = r Worksheets, version 1Worksheet PDFAnswer key PDF
- p(x + q) = r Worksheets, version 2Worksheet PDFAnswer key PDF
- p(x + q) = r Worksheets, version 3Worksheet PDFAnswer key PDF
Grade level and standard
Written for 7th grade math (expressions and equations) and aligned to CCSS 7.EE.B.4. It also works as review in later grades.
Common questions
- Is there an answer key?
- Yes. Every worksheet has a matching answer key with each answer worked on the same grid or layout as the question. The worksheet ID printed at the bottom of each page pairs a sheet with its key.
- Are any answers fractions?
- No. Every answer is a whole number, positive or negative, so students can check their work by substituting.
- Which method should students use for the bracket problems?
- Either. Dividing first is often quicker when the result is a whole number; distributing first always works. The answer key shows only the solution.
- How many different versions are there?
- About a million per skill. Each time you press the button the problems are generated fresh, so you can print a different version for every student, a retake, or another night of practice.
- Are the worksheets free?
- Yes. They are free to print and copy for your home or classroom, with no sign-up.