PRINCIPLES OF MATHEMATICS 11

PRE-CALCULUS 11Unit 6 – Day 3: ABSOLUTE VALUE EQUATIONS

Unit 6: Day 3 notes - Absolute Value EquationsPage 6 of 6

ABSOLUTE VALUE EQUATIONS

An absolute value equation is an equation that includes an absolute value of a variable expression.

The 2 cases to consider are when:

*The expression inside the absolute value symbol is positive or 0.

*The expression inside the absolute value symbol is negative.

SOLVING ABSOLUTE VALUE EQUATIONS GRAPHICALLY

ex 1:Solve  2x  3   =  5 graphically.

x

y 

4

0

-2

2

2

· Graph y  =   2x  3  and y  =  5

Answer: x = 1 or x = 4 ; solution set = { 1 , 4 }

ex 2:Solve  2x  3  = x graphically.

x

y 

0

3

-3

-3

3

SOLVING ABSOLUTE VALUE EQUATIONS ALGEBRAICALLY

To solve absolute value equations algebraically, use the mathematical definition of absolute value:

 x   =    

Ex 3:Solve  2x  3   =  5 algebraically.

Ex 4:Solve   2x  3  = x algebraically.

Answer: x = 1 or 3

Ex 5a:Solve  2x  3   =  4x algebraically.

Answer: x = 

Ex 5b:Solve  2x  3   =  4x graphically.

x

y 

4

0

-2

2

2

· Graph y  =   2x  3  and y  =  4x

Answer: x = Note where the extraneous root is on the graphs.

Ex 6:Solve   2x  3  = x algebraically.

[Answer: No solution]

Ex 7:Solve   x2  9  = 3x  9 algebraically.

[Answer: 3]

exercise:A packaging company rejects 200 mL juice packs when the actual amount of juice differs from the labelled amount by more than 5 millilitres. Write an absolute value equation that can be used to determine the greatest and least amount of juice that might be acceptable.

HW: p. 389 #1, 2, 4, 5ace, 6ace, 7, 9, 11, 15, 19, 20

exercise: The distance from a number x to the number 10 is 7 units on the number

line. Write an absolute value equation that models this scenario.

exercise: Write an absolute value equation that has 9 and 21 as its solution.

exercise: Write an absolute value equation that has -8 and 2 as its solution.

Answers:

xx

xx

³

ì

í

-<

î

if0

if0

1

2

7

10

=

-

x

6

15

=

-

x

5

3

=

+

x