Maths · Grades 6–8
Free one-step equations worksheets
Free printable one-step equations worksheets for grades 6 to 8: addition and subtraction, multiplication and division, mixed, negative numbers, fractions and decimals, balance-scale pictures, equations from words and word problems. Keys.
One-step equations: addition and subtraction
Sixteen equations of the form x + 7 = 12 and x − 5 = 9 with whole-number solutions to 20. Answer key on page 2. Free printable PDF.
One-step equations: multiplication and division
Sixteen equations of the form 4x = 28 and x/3 = 5 with whole-number solutions. Answer key on page 2. Free printable PDF.
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One-step equations: mixed practice
Sixteen equations mixing all four operations, so the student must decide which inverse to use. Answer key on page 2. Free printable PDF.
One-step equations with negative numbers
Twelve equations whose solutions or constants are negative, within −20 to 20, such as x + 5 = −3 and −4x = 20. Answer key on page 2. Free printable PDF.
One-step equations with fractions and decimals
Twelve equations with simple fractions and decimals (x + 1/2 = 2, 0.5x = 3), halves, thirds, quarters and tenths only. Answer key on page 2. Free printable PDF.
Balance the scales: picture equations
Eight balanced scales with x boxes and unit blocks; write the equation each shows and solve it. Answer key on page 2. Free printable PDF.
Write the equation from words, then solve
Eight sentences ("four times a number is 28") to turn into equations and solve. Answer key on page 2. Free printable PDF.
One-step equation word problems with a substitution check
Six word problems to model with a one-step equation, plus four given solutions to verify by substituting. Answer key on page 2. Free printable PDF.
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A one-step equation has one operation between x and the answer, so solving it means doing one thing: the opposite operation to both sides. These eight worksheets build that habit at a medium level (whole-number solutions to 20, integers within −20 to 20, fractions in halves, thirds and quarters, decimals to tenths) with a worked example on every sheet and the answer key on page 2. The set moves from addition and subtraction to multiplication and division, mixes them, adds negative numbers, then fractions and decimals, and finishes with three sheets that connect equations to meaning: balance scales, sentences to translate, and word problems with a substitution check.
What's in this set
- Addition and subtraction. Sixteen equations such as x + 7 = 12 and x − 5 = 9.
- Multiplication and division. Sixteen equations such as 4x = 28 and x/3 = 5.
- Mixed practice. Sixteen equations across all four operations; the student decides which inverse to use.
- With negative numbers. Twelve equations such as x + 5 = −3 and −4x = 20.
- With fractions and decimals. Twelve equations such as x + 1/2 = 2 and 0.5x = 3.
- Balance the scales. Eight balanced scales with x boxes and unit blocks: write the equation the picture shows and solve it.
- Write the equation, then solve. Eight sentences ("four times a number is 28") to translate and solve.
- Word problems. Six problems to model with a one-step equation, plus four given solutions to check by substitution.
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Teaching tips and common mistakes
How to use these worksheets
Print at 100%. Start with the balance scales if the idea of "both sides" is new; otherwise go in order. Ask for the check every time: substitute the answer back and read the equation aloud.
- Addition and subtraction. Say what was done to x, then undo it: "7 was added, so I subtract 7 from both sides." Writing the inverse operation under both sides keeps the equation balanced on paper.
- Multiplication and division. 4x means 4 times x; x/3 means x divided by 3. Undo by dividing or multiplying both sides. Watch for students who subtract the 4 from 4x.
- Mixed practice. The first decision is the whole exercise: which operation is attached to x? Have students name it before touching the pencil.
- Negative numbers. The same two rules work; the sign travels with its number. −4x = 20 means divide both sides by −4, so x = −5.
- Fractions and decimals. Same steps, different numbers. To undo 1/2 x, multiply by 2; to undo 0.5x, divide by 0.5 (or double). Answers are given as fractions in lowest terms or as decimals.
- Balance the scales. A box weighs x, each block weighs 1, and the beam is level. Taking three blocks off each side keeps it level: that is what "subtract from both sides" means.
- Write the equation from words. Sum means add, product means multiply, less than and decreased by mean subtract, half of means divide by 2. Translate, then solve.
- Word problems. Choose a letter, write the equation, solve, answer with a unit. The four substitution checks at the bottom show that a solution can be verified without a key.
Common mistakes to watch for
- Doing the operation to one side only. The equation is no longer true. The scales sheet makes the reason visible.
- Undoing with the same operation. x + 7 = 12 does not need another 7 added. Name the inverse first.
- Subtracting the coefficient. 4x = 28 is not x = 24. The 4 is multiplied, so divide.
- Sign slips with negatives. Keep the sign glued to its number and check by substituting.
Frequently asked questions
What grade are one-step equations for?
Grade 6 (6.EE.7, solving x + p = q and px = q with non-negative numbers), extended in grade 7 to negative numbers, fractions and decimals. The set follows that order: sheets 1 to 3 are grade 6, sheets 4 and 5 add the grade 7 numbers, and the last three suit both.
Do the worksheets have answer keys?
Yes. Every PDF has two pages: the worksheet and the same page with the answers filled in. The balance and word-problem keys also show the equation, not just the value of x.
What does "one-step" mean exactly?
One operation stands between x and a number, so a single inverse operation solves it: x + 7 = 12 or 4x = 28. Equations like 3x + 2 = 14 need two steps; those are on the two-step equations worksheets.
How hard are the numbers?
Medium on purpose. Solutions are whole numbers up to 20 (integers within −20 to 20 on the negatives sheet), fractions stay in halves, thirds and quarters, and decimals in tenths and quarters. The skill is the method, not the arithmetic.
Should students show working for a one-step equation?
Yes, at first: write the inverse operation under both sides, then the result. Once it is automatic, the answer plus a substitution check is enough.
More practice
Before equations: the order of operations worksheets teach the rules used to check a solution. After: the two-step equations worksheets. Fluent facts make the multiply-and-divide sheets quick: see the multiplication chart and division facts worksheets. For the numbers on sheet 5, the adding fractions and decimals worksheets.
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