1. Drill #8
Solve each equation 1. 2. 3.

2. Properties Example #2*
Solve each expression using the order operations. Name the property illustrated by each step.

3. Classwork Example #3*
Solve the expression using the order operations. Name the property illustrated by each step.

4. 1-5 Absolute Value Equations
Objectives: To solve equations involving absolute value.

5. Hyper vs. Hypo
Hypothermia 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 At what temperatures do these conditions begin to occur?

6. Absolute Value** Definition: For any real number a:
Case 1 (+): if a > 0 then |a| = a
Case 2 (–): if a < 0 then |a| = -a
The absolute value of a number is its distance to 0 on a number line.

7. (1.) Evaluating Absolute Value Expressions*
To evaluate an absolute value expression:
1. substitute all variables
2. evaluate the whole expression inside the absolute value
3. evaluate the absolute value
4. simpifly the expression
Example 1*: Evaluate:
|3x – 6| if x = -2

8. What is the value of | x – 15 |?
Make a list of the possible cases:
x = 19
x = 18
x = 17
x = 16
x = 15
x = 14
x = 13

9. What is the 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)
= 15 – x

10. (2.) Solving Absolute Value Equalities*
To solve an absolute value equality:
1. Isolate the absolute value
2. Make two cases (+ and – )
3. Solve each case
4. CHECK YOUR SOLUTION!!!!!!!!!
Example 2*: Solve the equation:
|x – 25| = 17, then check the solution.

11. Example 3*
Solve:
|2x + 7| + 5 = 0
Hint: Isolate the absolute value…

12. Example 4*
Solve:
| x – 2 | = 2x – 10

13. 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.