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Not Just Equals!
Not Just Equals!
Equations give you ONE answer: x = 5. But life often needs ranges! "You must be at least 16 to drive" means age ≥ 16. "The bag must weigh less than 23kg" means weight < 23. Inequalities describe these ranges - and we can solve them just like equations (with one important twist!).
Visual: Number Line Representations
Earn the mark scheme marks
Common Mistakes to Avoid
Wrong:
-2x > 6 becomes x > -3
Right:
-2x > 6 becomes x < -3 (flip when dividing by negative!)
Wrong:
Using closed circle for x < 5
Right:
Open circle for < and >, closed for ≤ and ≥
Wrong:
Integer solutions for -2 < x ≤ 3 include -2
Right:
-2 is NOT included (strict <), integers are -1, 0, 1, 2, 3
Now try it yourself
Quiz · Question 1 of 14
Which of the following correctly describes how to represent x > 3 on a number line?
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This topic in real past papers
Every real exam question we've found on linear inequalities, with a full worked answer.
AQA Paper 1
Three of the four sittings we have full papers for test a linear inequality, ranging from a one-step solve to a graphical region bounded by three inequalities.
Edexcel Paper 2
Two of the three sittings we have full papers for open with a linear inequality question, combining an algebraic solve with a number line diagram, and June 2023 adds a second algebraic solve worth 3 marks on its own.