Key points about one- and two-step linear equations
- Solving an A mathematical statement showing that two expressions are equal. The expressions are linked with the symbol =. means finding the value of an unknown A quantity that can take on a range of values, often represented by a letter, eg ๐, ๐ฅ, ๐ฆ, ๐ง, ๐ก โฆ etc. so that the equation is true.
- Equations are solved by using The opposite of a mathematical process. For example, the inverse of ร 5 is รท 5. The inverse operation undoes the original process.ย .
- Equations such as ๐ฅ โ 5 = 12 need one step to solve. Equations such as 3๐ฅ + 8 = 15 need two steps.
Make sure you are confident in calculating with negative numbers, which is a skill often needed to solve equations.
Check your understanding
Solving equations with one step
An equation is a mathematical statement showing that two A mathematical sentence made up of one or more terms expressed either numerically or symbolically. are equal. It includes an equals (=) sign, and an unknown An unknown value, usually represented by a letter such as ๐ or ๐., usually the letter ๐ฅ.
Solving an equation is the process of working out the value of ๐ฅ.
To solve an equation, The opposite of a mathematical process, eg, the inverse of ร 5 is รท 5. The inverse operation undoes the original process. are performed on both sides until the value for ๐ฅ is known.
The simplest equations have just one inverse operation to perform.
Follow the working out below
Exam style questions
- Solve x โ 8 = โ2.
๐ฅ = 6
To solve the equation, do the inverse operation. The inverse of subtracting 8 is adding 8. Adding 8 to both sides gives the solution x = 6.
- Solve 12๐ = 3.
๐ = \(\frac{1}{4}\)
To solve the equation, do the inverse operation. The inverse of multiplying by 12 is dividing by 12. A fraction line can be used to show โdivide byโ. Simplify the fraction by dividing the numerator and denominator by 3.
Game - One step equations
Practise your solving one step equation skills with these questions from our Divided Islands maths game.
Play the full Divided Islands game.
Solving equations with more than one step
Sometimes equations require more than one step to solve them.
The process of solving an equation involves isolating the An unknown value, usually represented by a letter such as ๐ or ๐. so that the letter terms are on one side of the equals sign, and the number terms are on the other.
To solve an equation, The opposite of a mathematical process, eg, the inverse of ร 5 is รท 5. The inverse operation undoes the original process. are performed on both sides until the value for ๐ฅ is known.
When solving an equation involves more than one step, the steps must be performed in the correct order.
The solution can be checked by In algebra, to replace a letter with a number. the answer into the original equation.
Follow the working out below
Exam style questions
- Solve 5๐ฅ + 12 = 2.
๐ฅ = โ2
- Subtract 12 from both sides.
- Divide both sides by 5.
- The solution is ๐ฅ = โ2.
- Check the answer by substituting โ2 in place of ๐ฅ in the original equation:
5๐ฅ โ 2 + 12 = โ10 + 12 = 2
- Solve 2๐ฆ + 5๐ฆ โ 100 = 180.
๐ฆ = 40
- Simplify the left-hand side by collecting the ๐ฆ terms together.
- Add 100 to both sides.
- Divide both sides by 7.
- The solution is ๐ฆ = 40.
- Check the answer by substituting 40 in place of ๐ฆ in the original equation:
2 ร 40 + 5 ร 40 โ 100
= 80 + 200 โ 100
= 180, so the answer is correct.
Game - Two step equations
Try these questions from our Divided Islands game and practise your solving two step equation skills.
Play the full Divided Islands game.
Quiz โ Solving one- and two-step equations
Practise what you have learned about solving one- and two-step equations with this quiz.
Now you have revised how to solve one- and two-step equations, why not take a look at formulae?
GCSE Maths resit revision
Revise for your resits with quizzes, flashcards and exam-style questions.
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