# Inequalities | Revision

A question can ask to find a set of values which satisfy an inequality equation. If the equation is a quadratic expression, then you should always sketch a graph in order to achieve your answer.

The graph above shows a small sketch of y = (x – 1) (x + 5)

Important Rule:

The red shaded area shows one set of values for x, the curve is below the x-axis, so y < 0

The green shaded areas show another set of values for x, the curve is above the x-axis, so y > 0.

There are a total of two separate set of values that satisfy this inequality. You will need to mention both these set of values and write ‘or’ between them.

1) Rearrange the equation so one side is equal to 0

2) Factorise the other side of the equation

3) Proceed to sketch the graph

4) Write down the solutions using the appropriate inequality symbol

Simple Inequality Question: (Basically solving a normal equation)

Find the set values for: (2 marks)

8x – 7 < 5x + 5

-5x

3x -7 < 5

+7

3x < 12

12 / 3 = 4

X < 4

Inequality Question with Sketched Graph:

Find the set of values for which:

2x2 – 5x – 3 > 0 (0 is already on one side so no need to rearrange)

(2x + 1) (x – 3) (Factorising the equation above)

X = -0.5 or x = 3 (Finding the roots in order to draw graph)

Draw the graph:

Answer: X < -0.5 or x < 3

Find the set values of both:

8x – 7 < 5x + 5 and 2x2 – 5x – 3 > 0

As you have already worked out the values of each individual equation, you can use an inequality line graph to determine the set of values for both of these inequalities:

This shows that:

X < =0.5 or 3 < x < 4

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