2.2-2.3 - Solving Absolute Value Equations and Inequalities

|v + 8| − 5 = 2

• $x=-1\ \ \ ,\ \ \ \ x=-15$

• $x=-1\ \ \ ,\ \ \ x=-5$
  

• $x=15\ \ \ ,\ \ \ x=-15$
  

• No Solution

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.A.1

CCSS.HSA.REI.B.3

|2a - 10| = 6

• a = 8, a = 5
• a = 2
• a = 8
• a = 8, a = 2

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.A.1

CCSS.HSA.REI.B.3

| x + 9 | = -5

•  $x=-14$  

•  $x=-4$  

•  $x=-14\ \ \ ,\ \ \ x=4$  

•  $no\ solution$  
  

Tags

CCSS.HSA.REI.B.3

−2|−2r − 4| = -12

• $r=5\ \ ,\ \ r=1$

  
  

• $r=-5\ \ ,\ \ r=1$

• $r=-5$

• No Solution

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.A.1

CCSS.HSA.REI.B.3

∣ 2x + 9 ∣ = 15

• x = 3 
• x = 3
  x = -6
• x = 3
  x = -12
• x = 6
  x = -12

Tags

CCSS.HSA.REI.A.1

CCSS.HSA.REI.B.3

3| −8x| + 8 = 80

• $x=-\frac{7}{3}\ \ \ ,\ \ \ x=\frac{7}{3}$

• $x=3\ \ \ ,\ \ \ x=-3$

• $x=\frac{11}{3}\ \ \ ,\ \ \ x=-\frac{11}{3}$

• No Solution

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.A.1

CCSS.HSA.REI.B.3

 $\left|4x-15\right|=\left|x\right|$  

•  $x=5\ \ \ or\ \ \ x=3$  

•  $x=-5\ \ \ or\ \ \ x=-3$  

•  $x=5\ \ \ or\ \ \ x=-3$  

•  $x=-5\ \ \ or\ \ \ x=3$  

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.A.1

CCSS.HSA.REI.B.3

Solve:

|x + 3| > 8

• x > 5 or x < -11

• x > 5

• x < 5 or x > -11

• no solution

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

| 2w - 1 | < 11

• No Solution

• 5 < w < 6

• -5 < w < 6

• -6 < w < 5

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.3

CCSS.HSA.REI.B.3

| x + 3 | ≤ 2

• No Solution
• All Real Numbers
• -5 ≤ x ≤ -1
• 1 ≤ x ≤ 5

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.3

CCSS.HSA.REI.B.3