Tues 131 SWBAT solve absolute value equations Agenda

Tues, 1/31 SWBAT… solve absolute value equations Agenda 1. WU (10 min) 2. 5 Examples: absolute value equations (25 min) 3. Exit slip (10 min) Warm-Up: 1. Take out back of agenda 2. Set-up notes. Topic = Solving absolute value equations HW#1: Absolute value equations

Solving Absolute Value Equations Ms. Sophia Papaefthimiou Infinity HS

Definition of Absolute Value The distance from any number to zero on the number line. n The value is always positive. Why? n

Ex. #1 |x| = 4 x = 4 or x = -4 To solve an absolute value equation: 1. Isolate the absolute value on one side of the equal sign. 2. Case 1: Set the expression inside the absolute value symbol equal to the other given expression. Solve. 3. Case 2 : Set the expression inside the absolute value symbol equal to the negation of the other given expression. Solve. 4. Check both solutions. Check: |x | = 4 or |x| = 4 | 4 | = 4 | -4 | = 4 4 = 4

Ex. #2 |x + 3| = 7 To solve an absolute value equation: 1. Isolate the absolute value on one side of the equal sign. 2. Case 1: Set the expression inside the absolute value symbol equal to the other given expression. Solve. 3. Case 2 : Set the expression inside the absolute value symbol equal to the negation of the other given expression. Solve. 4. Check both solutions. x + 3 = 7 or x + 3 = -7 x = 4 or x = -10 Subtract 3 from both sides Check: |x + 3| = 7 or |x + 3| = 7 | 4 + 3| = 7 | -10 + 3| = 7 |7| = 7 |-7| = 7 7 = 7

Ex. #3 |15 – 3 x| = 6 15 – 3 x = 6 or 15 – 3 x = – 6 The value of 15 – 3 x can be 6 or – 6 since |6| and |– 6| both equal 6. – 3 x = – 9 – 3 x = – 21 Subtract 15 from both sides. x = 3 or x = 7 Divide both sides by – 3. Check: |15 – 3 x| = 6 |15 – 3(3)| = 6 |15 – 3(7)| = 6 |6| = 6 |– 6| = 6 6 = 6

Ex. #4 | x | - 6 = -3 | x | = 3 Add 6 to both sides x = 3 or x = -3 Check: |x | - 6 = -3 or |x| - 6 = -3 | 3 | = 3 | -3 | = 3 3 = 3

Ex. #5 2| x | = -10

Absolute Value and No Solutions Absolute value is always positive (or zero). An equation such as │x │= -5 or │x – 4│= -6 is never true. n It has NO solution. n n │x │= -5 has no solution This is a distance And this is negative Ever heard of a negative distance? ? ?

Exit Slip Complete on a separate sheet of paper Solve and check: 1. ) │2 x + 4│ = 12 2. ) 3│x│= 6 3. ) │2 x + 4│ = -12 4. ) │3 c│- 45 = -18 5. ) │2 x + 4│ - 12 = -12