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!

𝒏𝟐−𝟒≥𝟑

𝒏𝟐−𝟒≤−𝟑or

+4 +4 𝒏𝟐≥𝟕𝟐 ∙ ∙𝟐

n 14 or

+4 +4 𝒏𝟐≤𝟏𝟐 ∙ ∙𝟐

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

𝒙<−𝟓𝒐𝒓 𝒙>𝟗

Ineq #1: Keep Ineq #2: KFC!

7

SWBAT: Solve Absolute Value Inequalities

−𝟐 .𝟖≤𝒅 ≤𝟐

Eq #1: Keep Eq #2: KFC!

𝟓𝒅+𝟐𝟑

≤𝟒𝟓𝒅+𝟐𝟑

≥−𝟒and𝟑 ∙ ∙𝟑

5𝑑+2≤𝟏𝟐-2 -2

d 2

5d 10 5 5

𝟑 ∙ ∙𝟑

5𝑑+2≥−𝟏𝟐-2 -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

−𝟑|𝒙−𝟖|−𝟑

<−𝟐𝟒−𝟑

8

𝒙<𝟎𝒐𝒓 𝒙>𝟏𝟔

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

|𝟑𝒎−𝟔|<𝟏𝟖Isolate 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

−𝟒<𝒎<𝟖and

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

𝒙𝒙

Eliminate 2&3, bc

those are for less than’s!

10x - 20 -30 10x -10 x -1

10x - 20 30 10x 50 x 5

OR

|𝟏𝟎𝒙 −𝟐𝟎|≥𝟑𝟎

x -1 or x 5