1. Ch. 3 â Inequalities
3.1 Linear Inequalities;
Absolute Value
Objectives:
Solve and graph linear inequalities in one variable
2. Solving Inequalities
âą Solve just like an equation, EXCEPT:
âą The inequality sign must be reversed if you
multiply or divide by a negative number
Graphing solutions
âą On a number line:
âą < , > use open circle
âą ïŁ , ïł use closed circle
âą Shade (or use an arrow) to indicate solution
set.
3. Example 1a
âą Solve 3x â 4 ïŁ 10 + x and graph the
solution.
6. Absolute Value
âą |x| means (geometrically) the distance
from x to zero on the number line. (c ïł 0)
Sentence Meaning
The distance
from x to 0 is:
Graph Solution
|x| = c exactly c units x = c or x = -c
-c 0 c
|x| < c less than c units -c < x< c
|x| > c greater than c
units
x < -c or x > c
-c 0 c
-c 0 c
7. âą Sentences with |x â k| can mean the
distance from x to k on the number line.
Sentence Meaning Graph Solution
|x - 5| = 3 The distance
from x to 5 is 3
units
x = 2 or x = 8
|x - 1| < 2 The distance
from x to 1 is
less than 2 units
-1 < x< 3
|x + 3| > 2 or
|x â (-3)| > 2
The distance
from x to -3 is
greater than 2
units
x < -5 or x > -1
8. Algebraic Method
Sentence Equivalent Sentence
|ax + b| = c ax + b = ï±c
|ax + b| < c -c < ax + b < c
|ax + b| > c ax + b < -c or ax + b > c
9. Example 2a
âą Solve |3x â 9| > 4 and graph the solution.
10. Example 2b
âą Solve |2x + 5| ïŁ 7 and graph the solution.
11. You Try!
âą Solve and graph the solution:
âą |2x + 3 | = 1
âą |x â 2| ïł 3