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.
Quadratic Inequality Steps:
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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