Maths · Grades 7–9
Free two step equations worksheets
Nine two-step equations worksheets for grades 7 to 9, all with answer keys: 20-problem practice sets, negatives and x/a, integers, fractions, decimals, multiple choice, eight word problems and a one-step and two-step mixed review.
Two-step equations multiple choice: 3x + 7 = 16 style
Choose the correct solution from four options for equations such as 3x + 7 = 16 and 2y - 5 = 11; answer key on page 2.
Two-step equations with fractions and negatives: 15 problems
Solve for the variable in 15 equations such as v/2 - 9 = -12 and 6 - v/(-9) = -3 with negative terms; answer key on page 2.
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Two-step equations with integers: 14 problems with fractions
Solve 14 equations such as r/10 + 4 = 5, 3p - 2 = -29 and (k - 10)/2 = -7 with integer answers; answer key on page 2.
Two-step equations ax + b = c: 10 problems with work boxes
Solve for x in 10 equations such as 2x + 4 = 12 and 10 + 7x = 45 with positive whole numbers; work boxes and answer key on page 2.
Two-step equations with decimals: 12 problems
Solve 12 equations with decimal coefficients such as 0.4d + 2.9 = 1.5 and 4.7r + 16 = 27.28, plus n/22 - 1.8 = 7; answer key on page 2.
Two-step equations practice A: 20 problems with answers
Twenty two-step equations of the form ax + b = c and ax - b = c with positive whole-number solutions, plenty of working space and a full answer key on page 2. Free printable PDF.
Two-step equations with negative numbers and x/a
Twenty two-step equations that include negative solutions and the form x/a + b = c, for grade 7 to 8. Answer key on page 2. Free printable PDF.
Two-step equation word problems: 8 real-life problems
Eight word problems (gym fees, taxi fares, saving for a bike, perimeter) to translate into two-step equations and solve. Answer key gives the equation and solution. Free printable PDF.
One-step and two-step equations mixed review: 24 problems
Twelve one-step and twelve two-step equations shuffled together so students must decide how many steps each needs. Answer key on page 2. Free printable PDF.
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These nine two-step equations worksheets each come with an answer key on page 2 and run from whole numbers to decimals. The first is multiple choice: pick the correct solution from four options for equations such as 3x + 7 = 16 and 2y - 5 = 11. The second has 15 problems with fractions and negative terms, such as v/2 - 9 = -12. The third has 14 problems with integer answers, including r/10 + 4 = 5 and 3p - 2 = -29. The fourth is the gentlest: 10 equations in the form ax + b = c with positive whole numbers, such as 2x + 4 = 12 and 10 + 7x = 45, each with a work box for showing steps. The fifth has 12 equations with decimals, such as 0.4d + 2.9 = 1.5 and 4.7r + 16 = 27.28.
A two-step equation needs two inverse operations: undo the addition or subtraction first, then the multiplication or division. Start with the work-box sheet, then multiple choice, then the integer, fraction and decimal sheets.
Four more sheets (added 2026)
- Practice A: 20 problems. ax + b = c and ax - b = c with positive whole-number answers and room to show both steps. The sheet to hand out first.
- Negatives and division. Twenty equations with negative solutions and the form x/a + b = c, for grade 7 to 8.
- Word problems. Eight real-life problems (gym fees, taxi fares, saving for a bike, a rectangle's perimeter) to translate into an equation and solve.
- One-step and two-step mixed review. Twenty-four equations shuffled together so students decide how many steps each needs.
What Students Will Practice
- Solving ax + b = c with positive whole numbers, writing each step in a work box
- Checking a candidate answer by substitution on the multiple choice sheet
- Handling negative constants and negative solutions, such as 3p - 2 = -29
- Undoing division when the variable sits in a fraction, as in r/10 + 4 = 5 and (k - 10)/2 = -7
- Working with decimal coefficients and constants, such as 0.4d + 2.9 = 1.5
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How to Use These Worksheets
Tips to help students build confidence with two-step equations.
- Teach the "reverse order of operations" rule: whatever was done last to build the expression gets undone first. In 3x + 5, the 5 was added last, so subtract it first. Then undo the multiplication by 3. This gives students a reliable method instead of guessing.
- Have your child write each step on a separate line and show what they did to both sides. Writing "subtract 5 from both sides" before doing it slows them down enough to avoid careless errors.
- After solving, always substitute the answer back into the original equation to verify. If 3(5) + 5 = 20 checks out, they know the answer is correct. This habit catches mistakes before they become patterns.
Common Mistakes to Watch For
- Performing operations on only one side of the equation. A student might subtract 5 from the left side but forget to subtract it from the right, writing 3x = 20 instead of 3x = 15. Stress that both sides must always stay equal.
- Doing the steps in the wrong order, dividing before subtracting. In 3x + 5 = 20, dividing everything by 3 first gives x + 5/3 = 20/3, which is messy and confusing. Always undo addition/subtraction before multiplication/division.
- Sign errors with negative numbers. In 2x - 8 = -4, students add 8 to both sides to get 2x = 4 (correct), but some write 2x = -12 because they subtracted instead of added. Highlight the inverse operation each time.
- Forgetting that dividing a negative by a positive gives a negative result. In -3x = 12, the answer is x = -4, not x = 4. Students often drop the negative sign during the final step.
Frequently Asked Questions
What should my child know before starting two-step equations?
They need to be comfortable with one-step equations (x + 5 = 12 or 3x = 21) and basic operations with negative numbers. If one-step equations feel shaky, review those first. Two-step equations build directly on that foundation.
How do I explain why we do the same thing to both sides?
Use a balance scale analogy. The equals sign is the center of the scale. If you take something off one side, you must take the same amount off the other side, or the scale tips. This visual helps the concept stick.
How many problems per practice session?
Start with 6-8 problems. If your child is getting them right consistently, add problems with negatives or fractions to increase the challenge. If they are making the same mistake, pause and fix that specific error before continuing.
When should I let my child use a calculator?
Not for the whole-number, integer and fraction sheets. Those involve basic arithmetic with small numbers, and doing the math by hand reinforces number sense. The decimals sheet (0.4d + 2.9 = 1.5 and similar) is the one place a calculator is reasonable, for checking the arithmetic once the steps are written out.
After mastering two-step equations, students move on to multi-step equations that involve combining like terms and using the distributive property before isolating the variable. For an equation with a real shape behind it, the Pythagorean theorem worksheets have students solve a² + b² = c² for a missing side.
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