Solving One and Two Step Equations
Solving an equation means finding the value of the unknown letter that makes both sides equal. A one-step equation needs a single inverse operation to solve, such as x + 5 = 12, while a two-step equation needs two inverse operations applied in the correct order, such as 3x + 5 = 20, where any addition or subtraction is undone before any multiplication or division.
Before you start
Make sure you're comfortable with these topics first:
Method
- Identify what has been done to the unknown, in the order the operations were applied, for example multiplied then added.
- Undo the operations in REVERSE order: undo any addition or subtraction first, then undo any multiplication or division.
- Whatever operation is done to one side of the equation, do exactly the same to the other side, to keep it balanced.
- Simplify each side after every step.
- Continue until the unknown is alone on one side of the equation.
- Check the solution by substituting it back into the original equation to confirm both sides are equal.
Worked example
Solve the equation 4x - 7 = 21.
- Identify the operations on x: it has been multiplied by 4, then had 7 subtracted.
- Undo the subtraction first by adding 7 to both sides: 4x - 7 + 7 = 21 + 7, giving 4x = 28.
- Undo the multiplication by dividing both sides by 4: 4x / 4 = 28 / 4, giving x = 7.
- Check: 4 x 7 - 7 = 28 - 7 = 21, which matches the right-hand side, so x = 7 is correct.
Practice questions
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Q1Solve x + 6 = 14.Show answer
Answer: x = 8
Q2Solve x - 9 = 5.Show answer
Answer: x = 14
Q3Solve 5x = 35.Show answer
Answer: x = 7
Q4Solve x/3 = 6.Show answer
Answer: x = 18
Q5Solve 2x + 3 = 17.Show answer
Answer: x = 7
Q6Solve 3x - 4 = 11.Show answer
Answer: x = 5
Q7Solve 5x + 1 = 26.Show answer
Answer: x = 5
Exam-style questions
Written in the style of a KS3 Maths exam paper, with a full mark scheme.
Solve the equation 6x + 5 = 41.
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Solve the equation 3x - 8 = 19.
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Amir thinks of a number. He multiplies it by 4 and then subtracts 9. His answer is 27. Form an equation and solve it to find Amir's number.
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Free printable worksheet
Want more practice on paper? Download the solving one and two step equations worksheet pack - 6 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 25 of KS3 Maths Workbook 1, the whole course as one free printable PDF.
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