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2.6 Absolute Value
Goals
SWBAT solve inequalities involving absolute value.
Definitions The of a,
denoted , is the distance that a is from zero on a number line.
The absolute value of a number is always.
So, in other words, and . That
said, we must consider both the negative and positive versions of a when solving absolute value equations and inequalities.
absolute value
a
positive
a a a a
Solve.
1. x 4 7
Solve
2. 12 3n 27
Solving Absolute Value Inequalities 1. Get the absolute value by itself, making
sure to remember that if you or by a negative
you flip the sign! 2. Set up two equality problems, one for the
positive, one for the negative, and solve. 3. Plot your solution(s) on a number line. Use
an dot for < or >, and a
dot for or 4. Test the intervals on your number line to
determine where to shade. (shade where it makes the statement true)
5. Write a compound inequality for your solution. (an and or an or)
multiplydivide
open closed
Solve the open set and graph its solution set.
3. v 5
2
Solve the open set and graph its solution set.
4. c 6 2
Solve the open set and graph its solution set.
5. 2n 9 7
Solve the open set and graph its solution set.
6. 1
3q 4 2
Solve the open set and graph its solution set.
7. 2 x 1
2 6
Solve the open set and graph its solution set.
8. 7 3c2
4