1. Absolute Value & Systems of Inequalities
Absolute Value Equations
Absolute Value Inequalities
Linear Inequalities

2. Absolute Value Equations and Inequalities
Distance from zero to n on a real number line.
|x| = 4 means, ‘ what number, x, are 4 units from zero on the number line.’

3. Absolute Value Equations
|u| = n
If n is positive then u = n or u = -n
Example: |x| = ; x = 2 or x = -2
However, if n is negative then the equation has no real solution.

4. |x + 7| = 4 2|x - 5| + 6 = 20 |m - 4| + 12 = 8 Practice
Solve the equation
|x + 7| = 4
2|x - 5| + 6 = 20
|m - 4| + 12 = 8

5. Application
Estella is driving from Savannah, Georgia to Washington D.C. Along the way, she will pass through Richmond VA. Estella’s distance from Richmond can be modeled by the function:
D(t) = |460 – 60t|
Find the time when Estella will be 40 miles from Richmond.

6. Absolute Value Inequalities
Inequality | x | < 5 , means all values of x that are less than 5 units from zero on the number line.

7. Absolute Value Inequality with < , <
Isolate absolute value inequality on one side
Rewrite as a compound inequality
|u| < n
-n < u < n

8. Absolute Value Inequality
Solve the inequalities. Give the solution as an inequality and graph the solution set on a number line.
|x - 4| < 6
|x + 3| + 8 < 10

9. Absolute Value Inequality > , >
‘Or’
Represents numbers further from zero
|x | > 5

10. Absolute Value Inequality
A person with high or low blood pressure will have a diastolic pressure (second number) that satisfies the inequality
|D - 75| > 15
Where D is a person’s diastolic pressure in millimeters of mercury (mmHg).
What is the high and low diastolic pressure?

11. Systems of Linear Inequalities
Two or more constraints on a give situation.
y > 2 x – 3
Graph
Solution
What does the solution mean?

12. Finding Inequalities from a graph