Download Unit 6 Notes Solving Absolute Value Equations 1

Algebra Part 3
Unit 6
Name____________________________
Date________________
Warm-up Solve and graph the inequalities.
1) 2x – 4 < 8
2) 3x – 4 > 2x + 5
3) -3x + x +2 <6
4) -2 < 2x + 2 < 8
Guided Notes
Unit 6 Notes – Solve Absolute Value Equations
Vocabulary
Absolute value of a number a, written ‫׀‬a‫׀‬, is the ___________________ between a and 0 on a number line.
Absolute value equation, ‫׀‬a‫ = ׀‬4, is an equation that contains an absolute value expression.
• The distance between a and 0 is 4
• The solutions of the equation are ____________ because they are the only numbers whose
distance from 0 is 4.
Example #1
│x│= 7
Solution
7 and -7
│x│= 3
Solution
__________
Example #2
│x - 3│= 8
Check your solution:
Example #3
Solve │2x - 7│- 5 = 4
Check your solution:
Guided Practice
Solve and check.
1. │y + 3│= 5
2. │7 - x│= 6
3. │r - 7│= 9
4. │12 + t│= 10
5. 4│t + 9│ = 19
6. 3│4x + 6│=18
Decide if an equation has no solution.
│3x + 5│+ 6 = -2
-6 -6
*subtract 6 from both sides
│3x + 5│= -8
***The absolute value of a number is never negative. So, there is no solution.
Homework: P. 393 #3 - 14