Pre-algebra and algebraGrade 7
Two-step equations worksheet with answer key
Equations in the form ax + b = c, with a smaller share written as x over d plus b. Choose positive-only or negative numbers, switch letters, set 6 to 30 problems, and print with an answer key.
- Fresh problems every time
- Answer key on its own page
- Print or PDF, Letter or A4
- Free, no sign-up
On this page
Two layers to peel
In a two-step equation the variable is wrapped in two operations. In 4x + 9 = 37, x is first multiplied by 4, then 9 is added. To solve, undo them in the reverse order: remove the 9, then remove the 4. Seventh graders learn this as "reverse order of operations," and it is the step that makes later multi-step equations manageable.
Students arrive here from the one-step version, and the single new idea is sequencing. A student who gets the order wrong will divide first, then have to deal with a fraction that did not need to be there.
What the sheet prints
Most lines look like ax + b = c, where a is a coefficient from 2 to 9 and b is a constant. About one in five lines is instead written as a fraction, x over d, plus b equals c, where d runs from 2 to 6. The student's answer line starts with "x = ".
- Equation type. The page starts on Two-step. Mixed adds one-step and multi-step problems if you want an all-in-one review.
- Include negative numbers. When off, every number and answer is positive, and about half the equations subtract the constant, as in 5x − 7 = 18. With it on, you will see forms such as −3x + 4 = 19 as well. Both the coefficient and the answer can be negative.
- Use different letters. Swap the x for y, n, a, m, k, p or t.
- Number of problems. 6 to 30, two per row. The default of 16 fills a page nicely.
Both kinds of constant appear with negatives off, so a class can practice undoing addition and undoing subtraction before signed numbers come in.
Worked example: 4x + 9 = 37
- Undo the addition. Subtract 9 from both sides: 4x + 9 − 9 = 37 − 9, which leaves 4x = 28.
- Undo the multiplication. Divide both sides by 4: x = 28 ÷ 4 = 7.
- Check. Substitute 7 into the original: 4 × 7 + 9 = 28 + 9 = 37. True.
A fraction version: x/4 + 3 = 8.
- Subtract 3 from both sides: x/4 = 5.
- Multiply both sides by 4: x = 20.
- Check: 20 ÷ 4 + 3 = 5 + 3 = 8. True.
With negatives on, try −3x + 4 = 19. Subtract 4 to get −3x = 15. Divide by −3, and the answer is x = −5. Check: −3 × (−5) + 4 = 15 + 4 = 19. True.
Spotting where a student went wrong
- Wrong order. Dividing 37 by 4 first gives a messy decimal. When a student reports a decimal and the key shows a whole number, the order is the likely cause.
- Dividing only one term. Turning 4x + 9 = 37 into x + 9 = 9.25 means the 4 was not applied to the 9.
- Sign slip with a negative coefficient. In −3x = 15, an answer of 5 means the student ignored the negative sign. The key shows −5.
- Skipping the check. The instruction line asks for substitution. Making this a rule means students catch their own mistakes before you do.
Related pages
If the setup feels easy, move on to the multi-step equations worksheet, which adds distribution and variables on both sides. Negative answers draw on integer rules, so the integers worksheet is a useful companion. A quick warm-up of order of operations shows why we undo steps in reverse.