Katherine Wu the absolute value of a number is its distance from 0 on a number line distance is nonnegative so the absolute value of a number is always positive symbol x is used to represent the absolute number of a number x ID: 778499
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Slide1
Lesson 1.4 - Solving Absolute Value Equations
Katherine Wu
Slide2the
absolute value of a number is its distance from 0 on a number line
distance is nonnegative so the absolute value of a number is always positive
symbol |x| is used to represent the absolute number of a number x
Example
1: Find the absolute value of 5.
|5| = 5
5 is 5 units away from 0, so |5| = 5.
Example 2: Find the absolute value of -8.|-8| = 8-8 is 8 units away from 0, so |-8| = 8.
5 units
8 units
| Absolute Value Equations |
Slide3| Absolute Value Equations |
some equations contain absolute value expressions
the absolute value of a number is always positive or zero, so an equation like |x| = -4 is never true. The solution for this type of equation is the
empty set
.the empty set is symbolized by { } or ø
Example 1: Solve |x + 12| = 9
x + 12 = 9 x + 12 = -9
x = -3 x = -21
Plug-In to Check
|-3 + 12| = 9
|9| = 9
x = -3 or -21
Example 2: Solve |x + 13| = -6|x + 13| ≠ -6x = øBecause an absolute value equation cannot result in a negative number|-21 + 12| = 9|-9| = 9
Slide4| Absolute Value Equations |
a
constraint is a condition that a solution must satisfy
equations can be viewed as the constraints of a problem
solutions of the equation meet the constraints of the problem
even if the correct procedure is used to solve an equation, the answers may not be the actual solutions to the original equation. This is called an
extraneous solution.
Example 1: Solve |2x + 12| = 4x
2x + 12 = 4x 2x + 12 = -4x
2x = 12 6x = -12
x = 6 x = -2
Plug-In to Check|2(6) + 12| = 4(6) |2(-2) + 12| = 4(-2)|24| = 24 |8| ≠ -8
There is only one solution; x = 6Example 2: Solve |x + 10| = 4x - 8x + 10 = 4x - 8 x + 10 = -(4x - 8)-3x = -18 5x = -2x = 6 x = -⅖Plug-In to Check|6 + 10| = 4(6) -8 |-⅖ + 10| = 4(-⅖) - 8
|16| = 16 |-9.6| ≠ -9.6
There is only one solution; x = 6
Slide5Practice 1: Solve |4x + 10| = 6x Practice 2: Solve 3|2a - 4| = 0
Practice 3: Find the absolute value of -24.
Practice 4: Find the absolute value of 0.
| Absolute Value Equations : Practice |
x = 5
a = 2
|-24| = 24
|0| = 0
Slide6GOOD LUCK
Go home and study for the final on Thursday