GCSE Maths · Topic guide
Solving Equations
Solving an equation means finding the value of the unknown letter that makes the equation true, by performing the same operation to both sides until the letter is on its own.
Method
- Decide what has been done to the unknown, then undo it using the inverse operation - the opposite of + is -, and the opposite of x is divide.
- Always apply the same operation to both sides of the equation, so it stays balanced.
- If the unknown appears on both sides, move all the letter terms to one side and all the number terms to the other side first.
- If there are brackets, expand them before collecting like terms.
- Once the equation reads (a number) x letter = (a number), divide both sides by that number to leave the letter alone.
- Check the answer by substituting it back into the original equation.
Worked example
Solve 3(x + 4) = 2x + 19.
- Expand the bracket: 3x + 12 = 2x + 19.
- Subtract 2x from both sides to collect the letters on one side: x + 12 = 19.
- Subtract 12 from both sides: x = 7.
- Check: 3(7 + 4) = 3 x 11 = 33, and 2(7) + 19 = 14 + 19 = 33. Both sides match, so x = 7 is correct.
Practice questions
Try each question, then tap to reveal the answer.
Exam-style questions
Written in the style of a GCSE exam paper, with a full mark scheme.
Q1[3 marks]
Solve 7x - 4 = 3x + 24. Show your working.
Q2[4 marks]
The angles of a triangle are x degrees, (x + 10) degrees and (2x - 40) degrees. Form and solve an equation to find x.
Next topics
Build a full practice pack.
This topic is one of hundreds in the library - pick the ones a student needs and generate a printable PDF in minutes.