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Solving Absolute
Value Inequalities October 8,
2015
SWBAT: Solve Absolute Value Inequalities
SWBAT: Solve Absolute Value Inequalities
2x - 6 = x + 3 or 2x - 6 = -(x + 3)
x - 6 = 3
x = 9 +6 +6
2x - 6 = -x - 3 +x +x
3x - 6 = -3
-x -x
3x = 3 3 3
x = 1
+6 +6
= x+3
CHECK
Isolate the abs. value first
SWBAT: Solve Absolute Value Inequalities
SWBAT: Solve Absolute Value Inequalities
SWBAT: Solve Absolute Value Inequalities
Yes!
No!
ineq #1: Keep
ineq #2: KFC!
2x + 3 2x + 3 and
-3 -3 2x 4
2 2 x 2
-3 -3 2x -10
2 2 x -5and
-5 x 2
7
SWBAT: Solve Absolute Value Inequalities
Yes!
No!
ineq #1: Keep
ineq #2: KFC!
ππβπβ₯π
ππβπβ€βπor
+4 +4 ππβ₯ππ β βπ
n 14 or
+4 +4 ππβ€ππ β βπ
n 2
n 2 or n 14 2
3
SWBAT: Solve Absolute Value Inequalities
x - 2 7 or x - 2 -7+2 +2
x 9
+2 +2
x -5
π<βπππ π>π
Ineq #1: Keep Ineq #2: KFC!
7
SWBAT: Solve Absolute Value Inequalities
βπ .πβ€π β€π
Eq #1: Keep Eq #2: KFC!
ππ +ππ
β€πππ +ππ
β₯βπandπ β βπ
5π+2β€ππ-2 -2
d 2
5d 10 5 5
π β βπ
5π+2β₯βππ-2 -2
d -2.8
5d -14 5 5
4
and
SWBAT: Solve Absolute Value Inequalities
No!
No!
Ineq #1: Keep Ineq #2: KFC!
11
x - 2 x - 2 and
+2 +2
x 13 and
+2 +2 x -9
-9 x 13
11
SWBAT: Solve Absolute Value Inequalities
No! 8
No!
ineq #1: Keep
ineq#2: KFC!
3x + 2 3x + 2 and -2 -2
3x 6
x 2
3 3and
-2 -2 3x -10
x
3 3
x 2
8
βπ|πβπ|βπ
<βππβπ
8
π<πππ π>ππ
Ineq #1: Keep Ineq #2: KFC!
x - 8 x - 8 or +8 +8
x 16
+8 +8 or x 0
Isolate the abs. value first
-24
SWBAT: Solve Absolute Value Inequalities
|ππβπ|<ππIsolate the abs. value first
Ineq #1: Keep Ineq #2: KFC!
3m - 6 3m - 6 and+6 +6
3 3 m 8
3 3
m -4
+6 +6
βπ<π<πand
SWBAT: Solve Absolute Value Inequalities
No! -4
Answer: All real numbers
SWBAT: Solve Absolute Value Inequalities
No! -3
Answer: No Solution
SWBAT: Solve Absolute Value Inequalities
SWBAT: Solve Absolute Value Inequalities
ππ
Eliminate 2&3, bc
those are for less thanβs!
10x - 20 -30 10x -10 x -1
10x - 20 30 10x 50 x 5
OR
|πππ βππ|β₯ππ
x -1 or x 5
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