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Exercises on linear equations solving for x

Learn how to solve linear equations step-by-step: remove parentheses, remove denominators, group terms, and isolate the variable. With solved examples and practice with instant correction.

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Linear equations: quick theory

A linear equation is an equality with an unknown (x) raised to the power of 1. Solving it means isolating x.

General method: 1) remove parentheses, 2) remove denominators by multiplying by the LCM, 3) group the terms with x on one side and the numbers on the other, 4) isolate x by dividing by its coefficient.

What is added is subtracted on the other side (and vice versa); what is multiplied is divided (and vice versa).

Step-by-step solved exercises on linear equations

Solved examples to show you the method. Then, practice with instant correction.

Exercise 1Solve 3x + 5 = 20.

Step-by-step solution

  1. We subtract 5: 3x = 20 − 5 = 15.
  2. We divide by 3: x = 15/3.
Solution: x = 5.

Exercise 2Solve 2(x − 3) = x + 4.

Step-by-step solution

  1. We remove parentheses: 2x − 6 = x + 4.
  2. We group: 2x − x = 4 + 6, meaning x = 10.
Solution: x = 10.

Exercise 3Solve (x + 1)/2 = 4.

Step-by-step solution

  1. We remove the denominator by multiplying by 2: x + 1 = 8.
  2. We solve: x = 8 − 1 = 7.
Solution: x = 7.

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This topic is studied in:

1st year of ESO2nd year of ESO3rd year of ESO

Frequently asked questions about linear equations

How do you clear denominators in an equation?

Multiply all terms by the least common multiple of the denominators. This eliminates the fractions and makes the equation easier to solve.

What does solving for x mean?

It means isolating x on one side of the equal sign. You move the numbers to the other side by doing the opposite operation (addition becomes subtraction; multiplication becomes division).

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