Drill 9 Solve each equation 1 2x 1

Drill #9 Solve each equation: 1. 2(x + 1) = – 3 ( x – 2) 2. 1 + (3 – x) = 2 – ( x + 1) Solve for the unknown variable: 3. for l 4. for x

Drill #10 Solve each equation: 1. 2. 1 – 2(2 x – 2 ) = x – ( 5 x + 5) Solve for the given variable: 3. for r 4. for x

Drill #11 Solve the following equations: Check your solutions! Simplify if x = -3 3. |5 x – 4| – x + 1 4. 10 – 2|– 6 – x|

Drill #12 Solve the following equations: Check your solutions! 1. 2 |x – 1| = 4 2. 3|x + 4| + 2 = 5 3. |2 x – 1| = x + 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)

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

Evaluate an Expression with Absolute Value: Example 1 Evaluate each of the following: Ex 1: 8 – |2 n + 5| if n = -3 Ex 2: |4 x + 3| – 3 if x = -2 Ex 3: ½ – |2 y + 1| if y = -¾

What is the absolute value of x ? Make a list of the possible cases: Case 1: If x > 0 so, |x| = x Case 2: If x < 0 so, |x| = –(x) or –x

What is the absolute value of x – 5? Make a list of the possible cases: Case 1: If x > 5 then x – 5 > 0 so, |x – 5|= x – 5 Case 2: If x is less than 5 then x – 5 < 0 so, x – 5 = -(x – 5) or 5 – x

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.

Solve an Absolute Value Equation: Examples Steps: 1. Isolate the absolute value 2. Set up 2 cases 3. Solve each case 4. Check your solutions! Ex 1: |2 x| = 4 Ex 4: |4 x + 2| = x – 3 Ex 2: 9 = |x – 12| Ex 5: 2|x + 3| + 4 = 2 Ex 3: -4 = -2| y + 5|

Solve an Absolute Value Equation: Examples Steps: 1. Isolate the absolute value 2. Set up 2 cases 3. Solve each case 4. Check your solutions! Ex 1: |2 x| = 4 Ex 2: 9 = |x – 12| Ex 3: -4 = -2| y + 5| Ex 4: |4 x + 2| + 5 = 15 Ex 5: 2|x + 3| – 4 = 2

Solve an Absolute Value Equation: Variable Expressions Steps: 1. Isolate the absolute value 2. Set up 2 cases 3. Solve each case 4. Check your solutions! Ex 1: |2 x| = x + 3 Ex 2: |x – 8| = x + 10 Ex 3: 2|x + 1| – x = 3 x – 4

Solve an Absolute Value Equation: Special Cases Steps: 1. Isolate the absolute value 2. Set up 2 cases 3. Solve each case 4. Check your solutions! Ex 1: |2 x + 4| = 0 Ex 2: |x + 10| + 5 = 5 Ex 3: 2|x + 1| = -4

Writing Absolute Value Equations from Word Problems • Find the value that is + or –. This will be the value that is on the opposite side of 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

Write an Absolute Value Equation: Example 1 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.

Hyper vs. Hypo: Example 2 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?