Drill #7 Solve: 1.-2(x – 4) = x – (3x – 8) Solve the following equations for the given variable: 2. 3(2s + t) = 4 for t 3. for x 4.xy + 1 = 4x + 3 for x

Drill #8 Solve the following equation for the given variable: 1.px + py = ax + ayfor x Evaluate the following absolute value expressions: If a = 3 and b = a – |b – a| 3. ab – a|b| 4.|ab| + |b – a|

1-4 Absolute Value Equations Objectives: To evaluate expressions involving absolute value and to solve absolute value equations. Homework: 1-4 Practice (#1 – 12)

What is absolute value? What is | -4 | ? What is | 4 | ? How do you evaluate -2 |(3)(-4) – 2| + 1

Example: Evaluating Absolute Value Expressions** Evaluate the following if a = -1 and b = 3 5 – | a – b| 1A: |2a + 2b| – 2a 1B: 1 – |a + b| 1C: |2b – a|

Classwork: Evaluate an Expression with Absolute Value Evaluate 8 - |2n + 5| if n = -5 1: |4x +3 | – 2 if x = -2 2: 1 - |4y – 1| if y = -¾

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.

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

Steps for Solving an Absolute Value Equation** ISOLATE the absolute value!!!! (get the absolute value by itself) Set up two cases (define a positive and a negative case) Solve each case (you should get two different solutions) Check the solution for each case (make sure each solution works)

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| 2C: 3|x – 2| = 122D: 2|x – 3| + 4 = 6

Example 3: Special Cases 1. Solve |x – 2| = 2x – |x – 2| + 1 = 1 3. | b – 3 | + 8 = 3

1-4 Solving Absolute Value Equations: Review of major points isolate the absolute value (if its equal to a neg, no solutions) set up two cases (the absolute value is removed) solve each case. check each solution. (there can be 0, 1, or 2 solutions)

Writing Absolute Value Equations from Word Problems* Find the value that is + or –. This will be the value that is equal to the abs. val. Find the middle value. This value will be subtracted from the variable in the abs. val. Example: expected grade = 90 +/- 5 points this translates to |x – 90| = 5 where x = test grade

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?

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.