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

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Presentation transcript:

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

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

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

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

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 98.6. At what temperatures do these conditions begin to occur?

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.

(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| + 3 if x = -2

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

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

(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.

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

Example 4* Solve: | x – 2 | = 2x – 10

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.