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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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Simplify both sides before gathering variable terms. Solve exactly, then round the final answer to the nearest hundredth when needed. Positive-only questions can still have negative solutions.

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A4

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Paper sizes and printing help · More equations activities

Choose the operands, then solve the relationship

Use x throughout or practice with different letters. Select constant magnitudes from 2–9 or 2–15 and coefficient magnitudes from 2–5 or 2–9. Choose signed questions or originals without negative operands or subtraction. These ranges describe the original factors and terms, not the expanded coefficients or final answers.

Positive-only inputs can still give a negative solution. For example, 2x + 3 = 5x + 9 has the solution x = −2. Every generated question has one solution; this set does not ask learners to classify identities or inconsistent equations.

Learning objective

What this activity builds

Simplify both sides, gather the variable terms on one side and use equality-preserving operations to find a unique solution.

Worked example

Solve 4(2x − 3) = 3x + 8.

x = 4.

Distribute: 8x − 12 = 3x + 8. Subtract 3x from both sides, then add 12: 5x = 20. Divide by 5. The original equation checks as 4(8 − 3) = 12 + 8, or 20 = 20.

Teaching notes

Make the practice count

  • Choose a consistent side on which to collect variable terms.
  • Explain subtracting a term from both sides instead of treating a sign change as a magic move.
  • Start with smaller operand ranges before increasing the arithmetic load.
  • Discuss why a positive-only input setting does not constrain the sign of the solution.

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Every setting combination makes ten unique equations with one solution. Positive mode removes printed negatives and subtraction.

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Math SheetNameScore/ 10TeacherDateVariables on Both SidesSolve exactly, then round the final value to the nearest hundredth.1.5r-3=2r-62.3(q+7)=5(q-3)3.3w+9=4(2w-6)4.5y+5=2y+45.4y+5y+2=3y+66.5f+7=3f+5f-57.2(k+3)=5(k-7)8.4w+4=2-5(w-5)9.5+5(r+2)=2r+210.5(2n+8)=4n-2math-sheet.comPage 1 / 1

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