1. 6.5 Solving Open Sentences Involving Absolute Value
What you’ll learn:
To solve absolute value equations.
To solve absolute value inequalities

2. Absolute Value Equations
Absolute value equations always involve 2 solutions. If the equation is 2x=10 then possible solutions are 5 and -5 because of the absolute value bars. Steps for solving an absolute value equation: 1. Create 2 equations. One looks just like the original equation without the bars. The other is set equal to the opposite. (= positive, = negative) 2. Solve each equation. FYI: Absolute value bars can never be equal to a negative number. The solution is “no solution.”

3. Solve x-5=7 x-5=7 x-5=-7 x=12 x=-2 3x=12 3x=12 3x=-12 x=4 x=-4
No solution!

4. Solving Absolute Value Inequalities
Decide if it’s an “and” or “or.”
(< , is and, >,  is or)
Separate into 2 inequalities with the word “and” or “or” between them. The first inequality looks the same. For the 2nd inequality change the sign of what it’s equal to and flip the inequality.
Solve and graph. (“and” should overlap, “or” usually doesn’t.

5. Solve and graph. x-53 It’s an “and” because of  x-53 and x-5-3
It’s an “or” because of 
2x or 2x-10
x or x-5
2x-1>5
2x-1>5 or 2x-1<-5
2x>6 or 2x<-4
x>3 or x<-2
3x<-3
No solution because the only numbers less than -3 are more negative and an abs. value can’t be negative!

6. Solve and graph.
x-62
3x-2<7
5x-15
2x-3>5

7. Classwork p all, all