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Example
2x2 + 7x + 6 < 0
Step 1 Factorise The Quadratic Expression
(2x + 3)(x + 2) < 0
Step 2 Equate The Quadratic Expression To Zero
(2x + 3)(x + 2) = 0
Step 3 Solve For Critical Values
(2x + 3) = 0 => x = -3/2
(x + 2) = 0 => x = -2
Step 4 Plot The Critical Values On A Number Line
Step 5 Decide Whether To Draw A U-Shaped Curve
Or An Inverted U-Shaped Curve
If the sign of x2 is positive - Then draw a U-shaped curve
If the sign of x2 is negative - Then draw an inverted U-shaped curve
2x2 is +ve => U-shaped curve
Step 6 Draw The Curve That Has Been Decided
Through The Critical Values On A Number Line
Step 7 Decide Whether You Want The U-Shaped Curve
Which Is Above Or Below The Number Line
If the question requires ax2 + bx + c < 0
Then we require the U-shaped curve below the number line
If the question requires ax2 + bx + c > 0
Then we require the U-shaped curve above the number line
The question requires 2x2 + 7x + 6 < 0
Thus we require the U-shaped curve below the number line
Step 8 Thicken The Required Curve
Step 9 State Values For Which The Inequality Is True
2x2 + 7x + 6 < 0
when x is greater than -2 but less than -3/2
which we can write as -2 < x < -3/2
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