Free one-step equations worksheets generator: addition and subtraction, multiplication and division, negative numbers, decimals, fractions and word problems, with answer keys.
Free one-step equations worksheets for 6th and 7th grade. Solve equations with addition and subtraction, multiplication and division, equations with negative numbers, decimals and fractions, plus one-step equations word problems. Every sheet has room for working, a new set of problems each time, and an answer key. There are also one-step equations with fractions and one-step equations word problems for students who are ready for more.
A one-step equations with negatives page, where x can be below zero.
Solve one-step equations online
Type the value of the variable (just the number is fine) and press Check.
Each of these one-step equations worksheets has an answer key. Choose Customize to load any sheet into the generator and switch the level, problem count or paper.
One-step equations: whole numbersLevel 1 + answer key.PDFCustomizeOne-step equations with negativesLevel 2 + answer key.PDFCustomizeOne-step equations: mixed formsLevel 3 + answer key.PDFCustomizeOne-step equations: addition and subtractionLevel 4: x + a = b and x − a = b.PDFCustomizeOne-step equations: multiplication and divisionLevel 5: ax = b and x/a = b.PDFCustomizeOne-step equations: with decimalsLevel 6: tenths, answer key included.PDFCustomizeOne-step equations: with fractionsLevel 7: fraction coefficients and sums.PDFCustomizeOne-step equations: word problemsLevel 8: write the equation, then solve.PDFCustomize
How to solve one-step equations
A one-step equation needs just one move to get the variable on its own. Ask what is being done to the variable, then do the opposite (the inverse operation) to both sides:
Equation
Do this to both sides
Answer
x + 7 = 12
Subtract 7
x = 5
x − 4 = 9
Add 4
x = 13
6x = 42
Divide by 6
x = 7
x ÷ 3 = 8
Multiply by 3
x = 24
Whatever you do to one side, do to the other, so the equation stays balanced like a pair of scales. Then check: put your answer back into the original equation and make sure both sides match. Every one of our one-step equations worksheets has an answer key, so students can check their own work.
One-step equations with addition and subtraction
When a number is added to the variable, subtract it from both sides. When a number is subtracted, add it back. For x + 15 = 32, subtract 15 to get x = 17. For n − 9 = 14, add 9 to get n = 23. Equations like 18 + x = 37 work the same way, because addition can be done in either order. The addition and subtraction level keeps every answer a positive whole number, which makes it the best place to start.
One-step equations with multiplication and division
4x means 4 times x, so divide both sides by 4 to undo it: 4x = 36 gives x = 9. A fraction bar means division, so x/5 = 7 is undone by multiplying both sides by 5, giving x = 35. Students often mix these up, which is why the multiplication and division worksheet mixes both forms on one page.
One-step equations with negative numbers
Integers make the same steps a little trickier. For x + 8 = 3, subtract 8 from both sides to get x = −5. For −6x = 42, divide by −6 to get x = −7. Remember the sign rules from integer worksheets: a positive divided by a negative is negative. The negative numbers level practices exactly this, and the mixed forms level also puts the variable on the right, as in 18 = x + 5.
One-step equations with decimals and fractions
Decimals follow the same rules. For y + 2.6 = 7.1, subtract 2.6 to get y = 4.5; for 0.5n = 3.5, divide by 0.5 to get n = 7. Keep the decimal points lined up when you subtract. With fractions, divide by the fraction or multiply by its reciprocal: for (3/4)x = 12, multiply both sides by 4/3 to get x = 16. For x + 1/8 = 5/8, subtract 1/8 to get x = 4/8, which simplifies to 1/2. Our one-step equations with fractions worksheet asks for every fraction answer in simplest form.
One-step equations word problems
Word problems turn a story into an equation. Choose a letter for the unknown, write the equation, then solve it. For example: “Movie tickets cost $8 each. Leo paid $40. How many tickets did he buy?” becomes 8t = 40, so t = 5. “After spending $12, Sam has $25 left” becomes s − 12 = 25, so s = 37. The one-step equations word problems level mixes stickers, tickets, pizza slices, recipes, ages and area, ten to a page with room for working.
One-step equations worksheets by grade
6th grade: writing and solving equations such as x + p = q and px = q with whole numbers, decimals and fractions (standard 6.EE.B.7 in the Common Core grade 6 expressions and equations). Start these one-step equations worksheets at levels 1, 4 and 5.
7th grade: equations with negative numbers and rational numbers, and word problems that lead to equations. Use levels 2, 3, 6, 7 and 8.
8th grade and up: a quick warm-up before two-step equations and multi-step equations.
Common mistakes to watch for
Doing the same operation instead of the inverse: for x + 6 = 10, adding 6 gives 16 instead of 4.
Changing only one side of the equation.
Dividing when the variable is divided: x/3 = 4 means multiply by 3, so x = 12, not 4/3.
Losing the negative sign in the final answer.
Skipping the check. Substituting the answer back takes ten seconds and catches most errors.
It is an equation you can solve with a single inverse operation, such as subtracting 7 from both sides of x + 7 = 12. Our one-step equations worksheets start with these and build up to negatives, decimals and fractions.
What does 4x mean?
4x means 4 times x. To undo it, divide both sides by 4.
How do you solve one-step equations with fractions?
Multiply both sides by the reciprocal of the fraction in front of the variable, or subtract the fraction if it is added. For (2/3)x = 10, multiply by 3/2 to get x = 15.
How do I check my answer?
Substitute it back into the original equation. If x = 7 for 6x = 42, then 6 × 7 = 42, so the answer is right.
What grade learns one-step equations?
Students usually start in 6th grade with whole numbers, decimals and fractions, then add negative numbers in 7th grade.
Do these one-step equations worksheets have answers?
Yes. The last page of every PDF, and of every set you build in the generator, lists the solutions, while the online practice marks each answer as soon as you press Check.
What comes after one-step equations?
Two-step equations, where you undo addition or subtraction first and then multiplication or division.
