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Linear Inequalities (OCR AS Maths: Pure)
Revision Note
Linear Inequalities
What are linear inequalities?
- Linear inequalities are similar to equations but answers take a range of values
- Linear means there will be no terms other than degree 1
- no squared terms or higher powers, no fractional or negative powers
- Inequalities use the symbols following symbols
- Greater than e.g.
- Less than e.g.
- Greater than or equal to
- Less than or equal to
- Inequalities can be represented in many ways using number lines, set notation and interval notation
Number line diagrams
- Number line diagrams are made up from circles and lines set above a number line
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- A filled-in circle or empty circle above a number denotes whether the number is included or not
- filled in for the greater/less than or equal to symbols
- empty for the greater/less than symbols
- Arrows show the range of values that are allowed
- A filled-in circle or empty circle above a number denotes whether the number is included or not
Set notation
- Set notation is a formal way of writing a range of values
- Use of curly brackets { }
- Intersection ∩ and union ∪ may be used
- Not to be confused with interval notation
Interval notation
- Interval notation uses different brackets to indicate whether a number is included or not
- Use of square [] and round () brackets
- [ or ] mean included
- ( or ) mean excluded
- (4,8] means 4 < x < 8
- Note ∞ always uses ( or )
- Not to be confused with set notation
Skills for solving linear inequalities
- representing and interpreting inequalities displayed on a number line
- writing and interpreting set notation
- eg {x : x > 1} ∩ {x : x ≤ 7} is the same as 1 < x ≤ 7
- writing and interpreting interval notation
- eg [-4, 6) is the same as -4 ≤ x < 6
How do I solve linear inequalities?
- Treat the inequality as an equation and solve
- avoid multiplying or dividing by a negative
- if unavoidable, “flip” the inequality sign so < → >, ≥ → ≤, etc
- try to rearrange to make the x term positive
Worked example
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