1. L1-5 Algebra 2

2. L1-5 Obj: Solve equations and inequalities involving absolute value
Distance from zero
Distance is positive
Example: Give all solutions to the equations
x = 7 or x = -7
no solution
x = 0

3. Solve |15 – 3x| = 6. Absolute Value Equations and Inequalities
LESSON 1-5
Additional Examples
Solve |15 – 3x| = 6.

4. Steps for solving absolute value equations
Isolate the absolute value
Rewrite the equation as two separate equations, one equal to the number, one equal to the opposite of the number
Solve each equation
Check your answers

5. Solve 4 – 2|x + 9| = –5. Absolute Value Equations and Inequalities
LESSON 1-5
Additional Examples
Solve 4 – 2|x + 9| = –5.

6. Solve |3x – 4| = –4x – 1. Absolute Value Equations and Inequalities
LESSON 1-5
Additional Examples
Solve |3x – 4| = –4x – 1.

7. Absolute Value Distance from zero
Abs > number means the distance from zero is great.
Abs < number means the distance from zero is small.

8. Additional steps for solving absolute value inequalities
If abs > number, write two inequalities with “or” in the middle
The first is the same without the bars
The second change the inequality and the sign of the other number
If abs < number, write a single inequality
Put the expression in the bars in the middle
Opposite of number < expression < number

9. Solve |2x – 5| > 3. Graph the solution.
Absolute Value Equations and Inequalities
LESSON 1-5
Additional Examples
Solve |2x – 5| > 3. Graph the solution.

10. Solve –2|x + 1| + 5 –3. Graph the solution. > –
Absolute Value Equations and Inequalities
LESSON 1-5
Additional Examples
Solve –2|x + 1| –3. Graph the solution.
> –

11. Absolute Value Equations and Inequalities
LESSON 1-5
Additional Examples
The area A in square inches of a square photo is required to satisfy A Write this requirement as an absolute value inequality.
< –
< –

12. Practice Solve (check for extraneous answers) |2x-3|=4x-1
Solve and graph |x-5|>8
Write an absolute value inequality 50<k<51
Homework: L1.5 (p 36) #8-38, 44-50e