Summary
Summary IEB AP Math:Rational Inequalities
This document describes: -How to approach rational inequalities with a systemtic adn reliable approach
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Rational inequalitiesSolve for:
(𝑥 − 2)(𝑥 − 3)
≥ 0 𝑤ℎ𝑒𝑟𝑒 𝑥 ∈ 𝑅
𝑥−4
We need critical values.
Critical values are values that will make the equation zero or product as error(0 in the
demoniator)
In this case:
𝑥 ≠ 4, 𝑥 = 2, 𝑥 = 3
Draw on a numberline:
𝑥 =2 𝑥=3 𝑥≠4
Solid dots means that the value is included(it is a valid value that does not produce
an error)
Hallow dots means that the value is excluded(it is a invalid as it causes a math error)
Now sub in values to which intervals produce what sign:
So:
x= 1
(1 − 2)(1 − 3)
1−4
(−1)(−2)
= −..
−3
Between the interval 𝑥 ∈ (−∞, 2], the sign is –
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