Inequalities
An inequality is a statement comparing two expressions with greater than, less than, or their or-equal-to versions, rather than stating they are exactly equal. In GCSE Algebra, students solve linear inequalities using the same steps as for equations, show solution sets on a number line, and list integer solutions, remembering to reverse the sign when multiplying or dividing by a negative number.
Before you start
Make sure you're comfortable with these topics first:
Method
- Treat the inequality like an equation: do the same operation (add, subtract, multiply, divide) to both sides to isolate the letter.
- If you multiply or divide both sides by a negative number, reverse the direction of the inequality sign.
- To solve a double inequality, such as -3 < 2x + 1 <= 9, apply each operation to all three parts at once.
- To list integer solutions, write out the whole numbers that satisfy the inequality, checking carefully whether the boundary values are included (<=, >=) or excluded (<, >).
- To show a solution on a number line, use an open circle for < or > since the boundary is not included, and a filled circle for <= or >= since it is included, then draw a line or arrow in the direction of the solutions.
- Check your answer by substituting a value from your solution set back into the original inequality.
Worked example
Solve the inequality 3(x - 2) >= 2x + 4.
- Expand the bracket: 3x - 6 >= 2x + 4.
- Subtract 2x from both sides: x - 6 >= 4.
- Add 6 to both sides: x >= 10.
Practice questions
Try each question, then tap to reveal the answer.
Exam-style questions
Written in the style of a GCSE Maths exam paper, with a full mark scheme.
Solve the inequality 6x - 5 <= 3x + 10.
n is an integer such that -4 <= n < 3. (a) List all the possible values of n. (2) (b) Write down the largest possible value of n. (1)
Solve the inequality -5 < 3x - 2 <= 10, and describe how the solution set would be shown on a number line.
See real past-paper questions on inequalities, organised by topic with official mark schemes →
Free printable worksheet
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