Lesson 20 Formulating Absolute Value Equations TEKS 2A.6D

Lesson 20 Formulate an Absolute Value Equation

TEKS 2A.6D

Poll

Bell ringer: If inverses on a graph reflect across the line, y=x, and inverses on a table and an equation simply switch the x and the y variable, what could be said of inverses domain and range?

• Nothing, this is a weird question...

• They stay the same for both the original function and the inverse.

• The domain and range switch just like the x and y's switch in inverses.

• Domain and range become smaller from the original to the inverse.

There is always a stationary number and a variation/deviation number.
These types of equations typically take the same format when using "everyday life" situations.

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​When formulating an Absolute Value equation...

​Equation setup:
|x-50|=5
50 is the stationary number in the equation and 5 is the variation/deviation number.

Multiple Choice

When Formulating Absolute Value Equations from a situation, they typically take which form?

• |x+stationary|=variation

• |x-stationary|=variation

• |x+variation|=stationary

• |x-variation|=stationary

So how do we know which number goes where??

Variation numbers are typically smaller and are preceded/followed by telling words such as plus or minus and more or less. In the case of our example it might be like "within 5 degrees"

​Variation/deviation Number:

Stationary numbers are the amount something SHOULD always be. For example...Reptiles like warm weather and their enclosures SHOULD always be close to 80 degrees Fahrenheit.

​Stationary Number:

Example 1

You have money in your wallet, but you don’t know the exact amount. When a friend asks you, you say that you have 50 dollars give or take $15.  Write an absolute value equation to model this situation.

Multiple Choice

You have money in your wallet, but you don’t know the exact amount. When a friend asks you, you say that you have 50 dollars give or take $15.  Write an absolute value equation to model this situation.

• |x-15|=50

• |x+50|=15

• |x-15|=50

• |x-50|=15

Poll

Why do we set the absolute value equation EQUAL to the deviation??

• You have to account for both the positive and negative, therefore it's easier to set the equation equal to the number that changes.

• When solving absolute value equations, we end up with two answers.

• When solving absolute value equations, we separate the equations into a "+" and "-" to solve for the variable since inside the absolute value symbol could be a + # or a - #..

• Math is magic

Multiple Choice

A pedestrian bridge is 53 meters long. Due to changes in temperature, the bridge may expand or contract by as much as 21 millimeters. Write an absolute-value to represent the minimum and maximum lengths of the bridge.

• |x+53|=0.021

• |x-0.021|=53

• |x-53|=0.021

• |x-53|=21

Multiple Choice

Lucia sets the thermostat in the apartment to 68 degrees. The actual temperature in the apartment can vary from this by as much as 3 degrees. Write an absolute- value to represent the lowest and highest temperatures that occur in the apartment.

• |x-68|=3

• |x+3|=68

• |x-3|=68

• |x+68|=3

Multiple Choice

The drama club set a goal for each member to sell 20 tickets to their play. The students with the highest and lowest actual sales were exactly 11 tickets from this goal. Write an absolute-value to represent both the highest and lowest number of tickets sold by an individual.

• |x-11|=20

• |x-11|>20

• |x-20|>11

• |x-20|=11

Multiple Choice

Victor has a goal of making $75 per week at his after-school job. Last month he was within $6.50 of his goal. What are the maximum and minimum amounts that Victor might have made last month? Write an absolute value equation representation.

• |75-x|=6.5

• |6.5-x|=75

• |x-75|=6.5

• |x-6.5|=75

Multiple Choice

Members of the track team can run 400 m in an average time of 58.2 seconds. The fastest and slowest times varied from the average by 6.4 seconds. What were the maximum and minimum times for the track team? Write an absolute value equation to represent this situation.

• |x-58.2|=6.4

• |x-6.4|=58.2

• |58.2-x|=6.4

• |6.4-x|=58.2