Page 27 - Math Course 3 (Book 1)

Absolute Value Inequalities
Mo. 1

Lesson 5 piecewise function
is a function whose definition changes depending
on the value of the independent variable.

KEY CONCEPTS: The absolute value function f(x) = | x | can be
1. Solve absolute value equations. –x if x < 0
written as f(x) = { x if x > 0

f(x) = 3 + | x – 2 | = { 3 + (x – 2) if x > 2
MO. 1 - L5a 3 – (x – 2) if x < 2
Solve Absolute Value Key Concept

Equations

Solving Absolute Value
Vocabulary A-Z Equations

Let us learn some vocabulary When solving equations that involve absolute value,
there are two cases to consider.

Case 1 The expression inside the absolute value
symbol is positive.
Absolute value
Case 2 The expression inside the absolute value
of any number n is its distance from zero on a
number line. The absolute value of n is written as symbol is negative.
| n |.

There are three types of open sentence
involving absolute value. They are | x | = n, Let’s Begin
| x | < n, and | x | > n

5 units 5 units
Solve an Absolute Value Equation

–6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6
Examples

Absolute value function

is a function written as f(x) = | x |, when f(x) ≥ 0 for WEATHER
all values of x. The average January temperature in a northern
Canadian city is 1 degree Fahrenheit. The actual
January temperature for that city may be about 5
f(x) = |x| degrees Fahrenheit warmer or colder.

x f(x) Solve |t – 1| = 5 to find the range of temperatures.

–3 3
Method 1 Graphing
–2 2
|t – 1| = 5 means that the distance between t and
–1 1 1 is 5 units. To find t on the number line, start at 1
and move 5 units in either direction.
0 0 The distance from 1 to 6 is 5 units.
The distance from 1 to –4 is 5 units.
1 1 The solution set is {–4, 6}.

2 2

3 3

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