Section 2­1 Word Problems.notebook
September 08, 2015
Section 2­1 Absolute Value Equations
Vocabulary - this is your bell work for today!
Absolute value ­ the absolute value of a real number x, written |x|, is its distance from zero on a number line.
Extraneous solution ­ An extraneous solution is a solution derived from an original equation that is not a solution to the original equation.
Section 2­1 Word Problems.notebook
September 08, 2015
Key Concept
Numbers
Symbols
|4| = 4
|x| = x, if x 0
|­4| = 4
|x| = ­x, if x < 0
Absolute Value Meaning
Equation
The distance between x and 0 is a units
|x| = a
Graph and Solution
­a 0 a
x = ­a and x = a Section 2­1 Word Problems.notebook
Problem 4
Formulating an Absolute Value Equation
Write an absolute value equation that represents each set of numbers.
1. all real numbers exactly 2 units from 4 2. all real numbers exactly 3 units from ­2
September 08, 2015
Section 2­1 Word Problems.notebook
September 08, 2015
Problem 4
Formulating an Absolute Value Equation
You drive 4 miles from home to the gym. After your workout, you drive to a grocery store that is x miles from your home on the same road as your home and gym. After buying some fruits and vegetables, you drive back to the gym where you have left your cell phone. So far, you have driven a total of 16 miles. Formulate an absolute value equation to represent this situation. you know you have driven 4 miles to the gym and 16 miles total. you know you drive some distance to the store "from the gym" |x­4|
just like in the last problems, "from the" is our starting value we make the trip twice from the store to the gym.. so 2|x­4|
16 = 4 + |x­4| + |x­4|
or 16 = 4 + 2|x­4| Section 2­1 Word Problems.notebook
Homework:
Page 38 : 2, 6, 12, 15, 16­28 evens, 32, 34
September 08, 2015