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Additional Mathematics
Algebra: Techniques

Section 1: Linear and quadratic inequalities

Notes and Examples
These notes contain subsections on
Linear inequalities
Quadratic inequalities

Linear inequalities
You already know that y = 2x + 1 is a straight line but what happens if we need
to look at y 2x + 1…

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AM Algebra Techniques 1 Notes and Examples


(iii) 11 3x + 5 20
11 3x + 5 and 3x + 5 20
Treat as two halves
6 3x and 3x 15
2 x and x 5
Therefore, 2x

You can see further examples using the Flash resource Linear inequalities.…

Page 3

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AM Algebra Techniques 1 Notes and Examples

Example 3
(i) a2 + 6 a + 5 0
(ii) p2 3p 10

Solutions Factorise Two quantities multiply to give
a negative; this implies that
(i) a2 + 6 a + 5 0 they are of different signs.
(a + 5)(a…






A good set of worked examples and explanation for solving linear and quadratic inequalities.  A written mistake in the initial paragraph which should say that the value of 2x +1 remains the same (rather than just x+1),  y is greater above the line or y is less below the line...  This may confuse if not corrected.

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