Practice Terms and variables
Variables stand for numbers, and expressions combine numbers, variables and operations.
They let you describe a general relationship instead of a single calculation.
Exercises with solutions
A term is an expression built from numbers, variables and operators. A variable is a placeholder for a value that can change. Like terms may be collected: 3x + 5x = 8x. Unlike terms may not: 3x + 5 stays as it is.
Exercise 1
Collect: 4x + 7x.
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11x
Both terms contain the same variable x, so you may add the numbers: 4 + 7 = 11.
Exercise 2
Collect: 6a + 3b + 2a.
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8a + 3b
Only the a-terms are alike: 6a + 2a = 8a. The b-term stays separate.
Exercise 3
What is the value of 5x + 3 for x = 4?
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23
Substitute 4: 5 · 4 + 3 = 20 + 3 = 23.
Exercise 4
Simplify: 3 · (x + 2).
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3x + 6
Distributive law: each term in the bracket is multiplied by 3, so 3 · x + 3 · 2.
Common mistake
Collecting unlike terms. 3x + 5 does not become 8x because the 5 has no variable. Only terms with the same variable may be added.
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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