Practice Linear equations
A linear equation can be solved by applying the same reversible operation to both sides until the variable is isolated.
Substitute the result into the original equation to check it.
Exercises with solutions
Apply the same transformation to both sides until x is isolated. Undo additions before factors when appropriate, then check by substitution.
Exercise 1
Solve 3x + 5 = 20.
Show solution and working
x = 5
Subtract 5 from both sides to get 3x = 15. Divide by 3. Check: 3 × 5 + 5 = 20.
Exercise 2
Solve 2(x − 3) = 10.
Show solution and working
x = 8
Divide both sides by 2: x − 3 = 5. Add 3. Check: 2 × (8 − 3) = 10.
Exercise 3
Solve 5x − 4 = 2x + 11.
Show solution and working
x = 5
Subtract 2x and add 4: 3x = 15. Divide by 3. Check: 25 − 4 = 10 + 11 = 21.
Exercise 4
A taxi charges €4 plus €2 per kilometre. The fare is €18. How far is the journey?
Show solution and working
7 km
Let x be the number of kilometres: 4 + 2x = 18. Subtract 4 and divide by 2: x = 7. Check: 4 + 2 × 7 = 18.
Common mistake
Changing only one side breaks the equality. When expanding brackets, multiply every term inside by the outside factor.
Free maths worksheets with worked solutions
Linear equations: free German worksheet with solutions (PDF)
From Grade 7: simple equations, brackets, variables on both sides and a word problem.
PDF and questions in German
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