1-4 Absolute Value EquationsObjectives: To solve inequalities using absolute value and to solve problems by making lists.

Hyper vs. HypoHypothermia and hyperthermia are similar

words but have opposite meanings. Hypothermia is defined as a lowered body temperature. Hyperthermia is an extremely high body temperature. Both are potentially dangerous conditions, and can occur when a person’s body temperature is more 8 degrees above or below the normal body temperature of 98.6. At what temperatures do these conditions begin to occur?

Evaluate an Expression with Absolute Value: Example 1

Evaluate each of the following:

Ex 1: 8.4 - |2n + 5| if n = -7.5

Ex 2: |4x +3 | - 3½ if x = -2

Ex 3: 1¼ - |2y + 1| if y = -¾

Classwork

1-4 Study Guide

ODD Problems

Absolute Value

Definition: For any real number a:

if a > 0 then |a| = a

if a < 0 then |a| = -a

The absolute value of a number is its distance to 0 on a number line.

Example 2: Solve an Absolute Value Equation

A standard adult tennis racket has a 100 square-inch head, plus or minus 20 square inches. Write and solve an absolute value equation to determine the least and greatest possible sizes for the head of an adult racket.

2A: 9 = | x + 12| 2B: 8 = | y + 5|

What is the absolute value of x – 15?

Make a list of the possible cases:

Case 1:

If x > 15 then x – 15 > 0

so, x – 15 = x – 15

Case 2:

If x is less than 15 then x – 15 < 0

so, x – 15 = -(x – 15) or 15 – x

Problem Solving Strategies**

Problem Solving Strategies

Draw a diagram Solve a similar problem

Make a table or chart Eliminate the possibilities

Make a model Look for a pattern

Guess and check Act it out

Check for hidden assumptions

Work backward

Use a graph Identify subgoals

List the possibilities

Rosa forgot the personal identification number (PIN) for her ATM card. She remembered that her PIN is the rearranged digits of her house number, which is 1256. What PIN’s should she try in the ATM?

Evaluate

Evaluate 3x – 6 + 3.2 if x = -2

Example*

Solve the equation:

x – 25 = 17, then check the solution.

Think about what cases the absolute value can be 17…

Examlpe*

Solve 2x + 7 + 5 = 0

Hint: Isolate the absolute value…

Example*

Solve x – 2 = 2x – 10

List the cases …

Check your answer …

Empty Set**

Definition: The set having no members, symbolized by { } or O

When an equation has no solution, the answer is said to be null or the empty set.