solve absolute value equations section 6.5 #44 there is nothing strange in the circle being the...
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Solve absolute value equations
Section 6.5
#44 There is nothing strange in the circle being the origin
of any and every marvel. Aristotle
Concept
We know absolute value as the distance a number is from zero
We have yet to use the arithmetic involved when solving for an interior variable
Today we’re going to talk about this concept on our path to further discussion of inequalities
Lets look and this Evaluate
3;2 xx
1
23
23
Absolute Value
• Absolute Value is the distance between a number and zero on a number line
5x
Solving with Absolute value Let’s solve this
5x
5xWhen working with absolute values, we
always have to account for the negative values
that satisfy the equation
5x
Solving with Absolute value When we look at this process, we essentially solve the
equation twice Once with the positive value Once with the negative value
5x
5x
2
53
x
x
Solving with Absolute value Let’s solve this
53 x
8
53
x
x
Bellwork Solution Solve for x
12 8x . 20, 4
. 4,20
. 20,4
.6,20
A
B
C
D
Bellwork Solution Solve for x
2 20 14x . 34, 3
. 17, 3
. 3,17
.3,17
A
B
C
D
2
42
512
x
x
x
Solving Inequalities This process however is only valid with the absolute
value is by itself
512
15123
x
x
3
62
512
x
x
x
Bellwork Solution Solve for x
4 8 16x . 16,16
. 4,4
. 4
.4
A
B
C
D
Bellwork Solution Solve for x
3 4 15 6x .1,7
. 3,11
.7,11
.13,24
A
B
C
D
ProcessRemove all the
outside components until
the absolute value is alone
Split the equation into two: one with
a positive the other negative
Solve as usual
Verify this answer makes
sense
?
Solving Inequalities We have to pay attention to situations that don’t exist
334 x
Solution No Absolute values can never be
negative, so this situation yields
no solution
Bellwork Solution Solve for x
4 15x . 11, 19
. 11,19
.11, 19
.
A
B
C
D NoSolutions
Bellwork Solution Solve for x
5 3 2 20x 23
23
. 2,
. 2,
.5,17
.
A
B
C
D NoSolutions
x
x
5.8
85.
Practical Example
85.
..
x
givenxdevabs
For this we use our understanding of absolute deviation which is given as
Minimum=7.5 psi
Maximum=8.5 psi
x
x
5.7
85.
givenxdevabs ..
Before the start of a professional basketball game, a basketball must be inflated to an air pressure of 8 pounds per square inch (psi) with an absolute error of .5 psi (Absolute error is the absolute deviation of a measured value from an accepted value.) Find the minimum and maximum acceptable air pressures for the basketball.
Practical ExampleA volleyball league is preparing a two minute radio ad to announce tryouts. The ad has an absolute deviation of .05 minute. Find the minimum and maximum acceptable times the radio ad can be.
..4 ,.8
.4 ,8
.1.5 ,2.5
.2
A m m
B m m
C m m
D m
Most Important Points What’s the most important thing that we can learn
from today? We can solve absolute value equalities by solving them twice,
once for the positive value, once for the negative value Absolute deviation can be expressed as the absolute value of
x minus the given value
Homework
6.51, 2-20 even, 21-32, 42-48