1. Day 3 ­ Absolute Value Inequalities
We know that the absolute value of a number is the distance that number is
from 0 on a number line.
Keeping that in mind, how would we find the solution and graph...
|x| ≥ 2 |x| < 2
­3 ­2 ­1 0 1 2 3
­3 ­2 ­1 0 1 2 3
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2. Solving an absolute value inequality is JUST like solving an absolute value
equation, but with one extra step!
Ex 1: 2 | x ­ 3 | ≤ 4
1st ­ Solve as if it were an equation
and get two answers. These two
solutions are called critical points.
2nd ­ Plot the critical points on a number
line and pick test points (tp) from
each of the three intervals that
have been created. ­10 ­9 ­8 ­7 ­6 ­5 ­4 ­3 ­2 ­1 0 1 2 3 4 5 6 7 8 9 10
**Always plug t.p. into ORIGINAL
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3. Ex 2: | 2x + 3 | > 7
1st ­ Solve as if it were an equation
and get two answers. These two
solutions are called critical points.
2nd ­ Plot the critical points on a number
line and pick test points (tp) from
each of the three intervals that
have been created. ­10 ­9 ­8 ­7 ­6 ­5 ­4 ­3 ­2 ­1 0 1 2 3 4 5 6 7 8 9 10
**Always plug t.p. into ORIGINAL
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