Practice Algebraic manipulation
Equivalent transformations rewrite an expression without changing its value, using arithmetic laws and combining like terms.
They make calculations and equations easier to handle.
Exercises with solutions
Combine only like terms, such as 3x and 2x, not 3x and 2y. Expand brackets by distributing the factor to every term. A minus before brackets changes every sign. Check by substituting a number.
Exercise 1
Simplify 3x + 2x − 4.
Show solution and working
5x − 4
3x + 2x = (3 + 2)x = 5x. The constant −4 remains.
Exercise 2
Simplify 2(3x − 4) + x.
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7x − 8
Multiply both terms inside by 2: 6x − 8 + x = 7x − 8.
Exercise 3
Simplify 5x − (2x − 3).
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3x + 3
Change both signs: 5x − 2x + 3 = 3x + 3. With x = 2, both expressions give 9.
Exercise 4
Factor out the greatest common integer factor from 6x + 9.
Show solution and working
3(2x + 3)
Both terms contain a factor of 3: 6x = 3 × 2x and 9 = 3 × 3.
Common mistake
3x + 2 is not 5x. Only combine terms with matching variables and powers. In −(2x − 3), the −3 changes to +3 as well.
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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