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One-step equations worksheet with integers
Print a 10-question one-step equations worksheet with signed integers, four inverse operations, exact answers, worked steps, and substitution checks.
Preview and downloadKeep both sides equal
Equation worksheets
Find the unknown, explain each operation and check the result. Start with one inverse operation, then add grouped quantities, distribution and variables on both sides.
Choose a worksheetOne relationship, equivalent equations
- Start3x + 5 = 20
- Subtract 5 from both sides3x = 15
- Divide both sides by 3x = 5
Show the reasoning
Undo one operation
Identify the operation acting on the unknown, then use its inverse on both sides. Choose one number domain or combine integers, decimals and fractions in one balanced sheet.
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One-step decimal equations worksheets
Practice ten one-step equations with decimal operands and exact terminating solutions. Use inverse operations and check each solution with the original decimal values.
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One-step fraction equations worksheets
Solve ten equations containing proper fractions and signed mixed numbers. Practice fractional coefficients and inverse operations, with exact working and answers rounded to hundredths.
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Mixed-number one-step equations worksheets
Build ten one-step equations from any nonempty mix of integers, decimals and fractions. The selected number types are balanced across the sheet, and every answer and substitution check stays exact.
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Follow a two-step relationship
Read a coefficient, an added quantity or a grouped numerator before deciding what to undo first. A fraction bar groups its entire numerator.
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Two-step equations worksheet
Print a 10-question two-step equations worksheet with integer quantities, fractional coefficients, grouped quotients, worked answers, and exact checks.
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Two-step decimal equations worksheets
Practice ten two-step equations with decimals, fractional coefficients and grouped division. Keep exact values during the solution and round the final answer to two decimal places.
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Simplify before solving
Distribute factors and collect like terms, including equations with variable terms on both sides. Choose eleven displayed structures for integer practice, or continue with decimal and focused both-sides questions. Keep each new line equivalent to the original.
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Multi-step integer equations worksheets
Choose from eleven equation structures for ten questions with integer operands. Practice like terms, grouped expressions and variables on either side, with exact worked solutions and separately rounded answers.
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Multi-step decimal equations worksheets
Choose from eleven equation structures for ten questions with signed half-step decimal operands. Practice like terms, grouped expressions and variables on either side, with exact worked solutions and separately rounded answers.
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Variables on both sides equations worksheets
Solve ten equations with the same variable on both sides. Choose the letter policy, constant and coefficient ranges, and signed or positive-only operands, with full worked solutions.
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Classify the solution set
Simplify equations with distribution, negation and repeated terms. Decide whether each has no solutions, one exact solution or infinitely many solutions.
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Determining equation solution types worksheets
Classify twelve linear equations as having no solutions, one solution or infinitely many solutions. Choose any nonempty combination, with exact rational roots on separate keys.
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Analyze and solve quadratic equations
Use the discriminant to predict the number and type of roots, then compare taking square roots, factorization, completing the square and the quadratic formula. Keep the displayed coefficients when calculating D.
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Working with the discriminant worksheets
Calculate the discriminant for twelve quadratic equations, then use its sign and square status to count and classify distinct roots. Choose monic, signed nonmonic or mixed leading coefficients.
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Solving quadratics by taking square roots worksheets
Solve ten quadratic equations by isolating a squared variable and taking both square roots. Choose direct, offset, scaled, multi-step or mixed equations with rounded real, exact real, no-real or imaginary results.
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Solving quadratics by factoring worksheets
Solve ten factorable quadratic equations with complete exact root sets. Choose factored form, expanded form, rearrangement practice or a balanced mixed sheet.
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Solving quadratics by completing the square worksheets
Solve ten quadratic equations by completing the square. Choose easy, hard or mixed equations and rational-only answers or exact radical roots.
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Solving quadratics with the quadratic formula worksheets
Solve ten quadratic equations with the quadratic formula. Practice original monic and nonmonic equations with rational and exact radical answers.
Preview and downloadRead the whole expression before solving
Absolute value equations
Choose among six families covering signed interiors, outside coefficients, fractional expressions and variable denominators. Read bar placement, keep domain exclusions and check every exact solution in the original equation.
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Absolute value equations worksheets
Solve ten absolute value equations from six selectable families. Practice signed interiors, outside coefficients, fractions and variable denominators, with exact solutions, clearly marked approximations and separate worked keys.
Preview and downloadBuild an equation from a story
Identify the unknown quantity before choosing an operation. A missing total, a missing group size and a missing number of groups can use the same multiplication relationship in different ways.
The expanded one-step story set includes quantities removed, unknown group counts and totals shared equally. Choose digits, number words or a mixture, and decide whether to include extra information.
Word problems
One-step equation word problems
Find a missing starting amount, part, total or unit cost in ten short stories. Choose digits, number words or a mixture, and optional irrelevant information.
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Word problems
Two-step equation word problems
Solve ten stories involving fixed fees and rates, budgets, halves and consecutive numbers. Choose number wording and print a separate answer key.
Preview and downloadUndo operations without changing the solution
In 3x + 5 = 20, the unknown is multiplied by 3 and then increased by 5. Undo the addition first: subtract 5 from each side. Divide both remaining sides by 3 to isolate x.
A fraction bar can group a whole expression. For (7 − x) ÷ 3 = 5, multiply both sides by 3 before dealing with 7 − x. After subtracting 7, the equation is −x = 8, so x = −8.
Separate exact solving from final rounding
The one-step integer, decimal and mixed-number sheets ask for exact answers. The fraction-only, two-step and multi-step sheets ask for answers to the nearest hundredth; their worked keys keep an exact value as well.
For 3x = 10, the exact solution is 10/3 and its rounded report is 3.33. Multiplying 3.33 by 3 gives 9.99, so that rounded number cannot provide an exact substitution check. Use 10/3 to verify the original equation.
Check in the original equation
Replace every occurrence of the variable with the exact solution. Evaluate the two original sides independently. Matching values confirm the answer for that equation and can reveal an earlier sign or distribution error.
For 4(2x − 3) = 3x + 8 and x = 4, the left side is 4(8 − 3) = 20, and the right side is 12 + 8 = 20. Both sides agree.
Choose by readiness
Start where the learner can explain the arithmetic
Grade 5–6 links are starting guides, not claims of alignment to a national curriculum. Fractional coefficients, signed distribution and variables on both sides may belong later in a local course.
Explain the inverse operation
Use a short equation to explain how one operation can be undone on both sides. Signed-number knowledge is needed.
Open this starting point →Keep decimal operations exact
Use familiar inverse operations with decimal operands and terminating solutions.
Open this starting point →Work with fractional coefficients
Interpret mixed numbers and reciprocals, then distinguish an exact fraction from a rounded decimal.
Open this starting point →Mix three number types
Balance integer, decimal and fraction equations while keeping every solution and check exact.
Open this starting point →Read the whole grouped quantity
Practice two-step equations, including fractional coefficients and a whole numerator divided by a constant.
Open this starting point →Connect distribution with solving
Move from expanding expressions to simplifying both sides of a complete equation.
Open this starting point →Use one letter and positive operands
Keep the visible inputs simpler while practicing variables on both sides. The resulting solution may still be negative.
Open this starting point →Use a short set to identify the next lesson
Model one equation aloud, ask the learner to explain the next, then use a ten-question sheet. Review the cause of an error before increasing difficulty: operation order, a signed coefficient, a fraction bar or a missed term in distribution.
Each resource includes ready-made Letter and A4 PDFs. Customize the seed, paper, available printed language and note below its teaching guide. Worked answers are separate pages, and the preview and download use the same questions.