Equations with Brackets and Unknowns on Both Sides
More advanced linear equations may contain brackets that must be expanded before solving, and the unknown letter may appear on both sides of the equals sign, which must be collected onto one side before the equation can be solved. Solving them combines expanding brackets, collecting like terms, and the balancing method used for simpler equations.
Before you start
Make sure you're comfortable with these topics first:
Method
- If the equation contains brackets, expand them fully first, taking care with negative signs outside a bracket.
- Simplify each side of the equation separately by collecting any like terms.
- If the unknown appears on both sides, choose the side with the larger coefficient of the unknown and add or subtract to move all unknown terms there, keeping the equation balanced.
- Move all number terms to the opposite side from the unknown, again applying the same operation to both sides.
- Simplify to reach the form (number)x = (number), then divide both sides by the coefficient of x.
- Check the solution by substituting it back into the original, unexpanded equation.
Worked example
Solve the equation 3(2x - 1) = 5x + 7.
- Expand the bracket on the left: 3(2x - 1) = 6x - 3, so the equation becomes 6x - 3 = 5x + 7.
- Collect the x terms onto the left by subtracting 5x from both sides: 6x - 5x - 3 = 7, giving x - 3 = 7.
- Add 3 to both sides: x = 10.
- Check: left side, 3(2 x 10 - 1) = 3 x 19 = 57. Right side, 5 x 10 + 7 = 57. Both sides match, so x = 10.
Practice questions
Type your answer and press Check to be marked straight away, or reveal the answer and mark yourself.
Q1Solve 2(x + 3) = 16.Show answer
Answer: x = 5
Q2Solve 5(x - 2) = 3x + 4.Show answer
Answer: x = 7
Q3Solve 4x + 3 = 2x + 15.Show answer
Answer: x = 6
Q4Solve 7x - 2 = 3x + 18.Show answer
Answer: x = 5
Q5Solve 3(x + 4) = 2(x + 9).Show answer
Answer: x = 6
Q6Solve 5x - 3 = 2(x + 3).Show answer
Answer: x = 3
Q7Solve 3(3x - 2) = 7x + 6.Show answer
Answer: x = 6
Exam-style questions
Written in the style of a KS3 Maths exam paper, with a full mark scheme.
Solve the equation 4(3x - 2) = 2x + 32.
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Solve the equation 5(x + 1) = 3(x + 7).
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A student solves the equation 2(x - 3) = 4x + 8 and gets the answer x = -7. Check the student's answer by substituting it back into the original equation, and state whether it is correct.
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Free printable worksheet
Want more practice on paper? Download the equations with brackets and unknowns on both sides worksheet pack - 7 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 26 of KS3 Maths Workbook 1, the whole course as one free printable PDF.
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