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One-variable linear equations practice

Solving a linear equation means undoing what was done to x, in reverse order, while keeping both sides balanced.

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How it works

A linear equation like 5x + 12 = 37 is a balance: whatever you do to one side, do to the other. Undo the operations in reverse order. Subtract 12 to get 5x = 25, then divide by 5 to get x = 5.

With messier equations, tidy up first:

  1. Clear fractions by multiplying both sides by the denominator (or by the LCM of all denominators).
  2. Distribute and combine like terms on each side.
  3. Collect the x terms on one side and the numbers on the other.
  4. Divide by the coefficient, and check by substituting back in.

One-Variable Linear Equations practice problems with solutions

These problems come from Mathyessy's question bank. Try each one before opening the solution.

  1. If 5x + 12 = 37, what is x?

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    Answer: 5

    Subtract 12: 5x = 25. Divide by 5: x = 5.

  2. If (6x + 14)/5 = 10, what is x?

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    Answer: 6

    Multiply both sides by 5: 6x + 14 = 50. Then 6x = 36, so x = 6.

  3. If 2(x+3) + 3(x−1) = 38, what is x?

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    Answer: 7

    Distribute: 2x + 6 + 3x − 3 = 38, so 5x + 3 = 38. Then 5x = 35 and x = 7.

  4. If 2x/3 + 6 = x, what is x?

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    Answer: 18

    Subtract 2x/3 from both sides: 6 = x/3. Multiply by 3: x = 18. Check: 12 + 6 = 18.

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