Post on 17-Jan-2016
transcript
October 31, 2012Solving Absolute Value Inequalities
DO NOW: Solve.1.
2. │x + 13│ = 8
3. │3x – 9│= -24
2
3x 4
HW 6.5b: Pg. 350 #29-39, skip 36 and 38Unit Test Monday, Nov 5
Lesson 6.5b Solving Absolute Value Inequalities with >, ≥ (greater)
Example 1: Graph the values for x that will satisfy the inequality. Then solve.
│x│≥ 3
5-4 -2 0 2 4-5 -3 1 5-1-5 3
“All values of x whose distance is 3 or more units away from zero.”
Try |x| > 5
Solving Absolute Value Inequalities with <, ≤ (less than)
Example 2: Graph the values for x that will make this true. Then solve.
|x| ≤ 3
5-4 -2 0 2 4-5 -3 1 5-1-5 3
“All values of x whose distance is 3 or less units away from zero.”
Try |x| < 5
Solving Absolute Value Inequalities
Example 3) Solve, then graph
|3x -12| ≥ 6
* Flip the inequality for the negative case.
20-15 -5 5 15-20 -10 10-20 200
Use the same steps you used to solve for Absolute Value Equations!
Set up 2 equations: each for the positive and negative solutions
This these!
1. Solve and graph |2x + 3| < 15
Step 1: Take the inside value and set the two cases, the positive and negative (flip the <)
Step 2: Graph the answer.
Step 3: Write the solution
2. Solve and graph |x – 4| ≥ 10
20-15 -5 5 15-20 -10 10-20 200
Step 1: Take the inside value and set the two cases, the positive and negative (flip the ≥)
Step 2: Graph the answer.
Step 3: Write the solution
The difference between|x| > n and |x| < n
|x| ≥ n (greater than) is n distance or more away from zero and an “OR” compound inequality.
graph OUT
│x│ ≤ n (less than) is within n distance from zero and an “AND” compound inequality.
graph IN
Start practicing on your homework.
HW 6.5b: Pg. 350 #29-39, skip 36 and 38