News
Get Premium
Dashboard

Dashboard Sign out
Big Ideas Math Integrated I, 2016
BI
Big Ideas Math Integrated I, 2016 View details
4. Solving Absolute Value Equations
Continue to next subchapter
search

Exercise 22 Page 32

How many cases do you have after you remove the absolute value?

Solutions: v=- 3 and v=6
Number Line:

Practice makes perfect
Before we can solve this equation, we need to isolate the absolute value expression using the Properties of Equality.
- 3|1-2/3v|=- 9
DivEqn

.LHS /(- 3).=.RHS /(- 3).

|1-2/3v|=3
An absolute value measures an expression's distance from a midpoint on a number line. |1-2/3v|= 3 This equation means that the distance from 1 is 3, either in the positive direction or the negative direction. 1-2/3v= 3 and 1-2/3v= - 3 To find the solutions to the absolute value equation, we need to solve both of these cases for v. Let's start with the positive case.
1-2/3v=3
â–Ľ
Solve for v
SubEqn

LHS-1=RHS-1

-2/3v=2
MultEqn

LHS * (-3/2)=RHS* (-3/2)

-2/3v(-3/2)=2(-3/2)
MultFracByInverse

a/b* b/a=1

v=2(-3/2)
MoveNegFracToNum

Put minus sign in numerator

v=2(-3/2)
DenomMultFracToNumber

2 * a/2= a

v=- 3
Similarly, we can solve the negative case.
1-2/3v=- 3
â–Ľ
Solve for v
SubEqn

LHS-1=RHS-1

-2/3v=- 4
MultEqn

LHS * (-3/2)=RHS* (-3/2)

-2/3v(-3/2)=-4(-3/2)
MultFracByInverse

a/b* b/a=1

v=-4(-3/2)
MoveNegFracToNum

Put minus sign in numerator

v=-4(-3/2)
MoveLeftFacToNum

a*b/c= a* b/c

v=- 4 (-3)/2
MultNegNegOnePar

- a(- b)=a* b

v=12/2
CalcQuot

Calculate quotient

v=6
Both - 3 and 6 are solutions to the absolute value equation. Let's graph these solutions on a number line.
Subchapter links expand_more
arrow_right Communicate Your Answer p.27
4
Communicate Your Answer 5 (Page 27)
arrow_right Monitoring Progress p.28-31
Monitoring Progress 1 (Page 28)
Monitoring Progress 2 (Page 28)
Monitoring Progress 3 (Page 28)
Monitoring Progress 4 (Page 29)
Monitoring Progress 5 (Page 29)
Monitoring Progress 6 (Page 29)
Monitoring Progress 7 (Page 29)
Monitoring Progress 8 (Page 30)
Monitoring Progress 9 (Page 30)
Monitoring Progress 10 (Page 31)
Monitoring Progress 11 (Page 31)
Monitoring Progress 12 (Page 31)
Monitoring Progress 13 (Page 31)
arrow_right Exercises p.32-34
Exercises 1 (Page 32)
Exercises 2 (Page 32)
Exercises 3 (Page 32)
Exercises 4 (Page 32)
Exercises 5 (Page 32)
Exercises 6 (Page 32)
Exercises 7 (Page 32)
Exercises 8 (Page 32)
Exercises 9 (Page 32)
Exercises 10 (Page 32)
Exercises 11 (Page 32)
Exercises 12 (Page 32)
Exercises 13 (Page 32)
Exercises 14 (Page 32)
Exercises 15 (Page 32)
Exercises 16 (Page 32)
Exercises 17 (Page 32)
Exercises 18 (Page 32)
Exercises 19 (Page 32)
Exercises 20 (Page 32)
Exercises 21 (Page 32)
Exercises 22 (Page 32)
Exercises 23 (Page 32)
Exercises 24 (Page 32)
Exercises 25 (Page 32)
Exercises 26 (Page 32)
Exercises 27 (Page 32)
Exercises 28 (Page 32)
Exercises 29 (Page 32)
Exercises 30 (Page 32)
Exercises 31 (Page 33)
Exercises 32 (Page 33)
Exercises 33 (Page 33)
Exercises 34 (Page 33)
Exercises 35 (Page 33)
Exercises 36 (Page 33)
Exercises 37 (Page 33)
Exercises 38 (Page 33)
Exercises 39 (Page 33)
Exercises 40 (Page 33)
Exercises 41 (Page 33)
Exercises 42 (Page 33)
Exercises 43 (Page 33)
Exercises 44 (Page 33)
Exercises 45 (Page 33)
Exercises 46 (Page 33)
Exercises 47 (Page 33)
Exercises 48 (Page 33)
Exercises 49 (Page 33)
Exercises 50 (Page 33)
Exercises 51 (Page 33)
Exercises 52 (Page 34)
Exercises 53 (Page 34)
Exercises 54 (Page 34)
Exercises 55 (Page 34)
Exercises 56 (Page 34)
Exercises 57 (Page 34)
Exercises 58 (Page 34)
Exercises 59 (Page 34)
Exercises 60 (Page 34)
Exercises 61 (Page 34)
Exercises 62 (Page 34)
Exercises 63 (Page 34)
Exercises 64 (Page 34)
Exercises 65 (Page 34)
Exercises 66 (Page 34)
Exercises 67 (Page 34)