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Warm-up: 9/17. The ideal length of a bolt is 13.48 cm. The length can vary from the ideal by at most 0.03cm. A machinist finds one bolt that 13.67 cm long. By how much should the machinist decrease the length so the bolt can be used?. Standard: A.CED: Create equations and inequalities in one

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Warm up 9 17

Warm-up: 9/17

The ideal length of a bolt is 13.48 cm. The length can vary from the ideal by at most 0.03cm. A machinist finds one bolt that 13.67 cm long. By how much should the machinist decrease the length so the bolt can be used?


Standard: A.CED: Create equations and inequalities in one

variable including ones with absolute value and use them to

solve problems. Include equations arising from linear and

quadratic functions, and simple rational and exponential functions.

Objective: To solve absolute value equations and inequalities

Absolute value: of a number is its distance from zero on the

number line and distance is nonnegative.

So x = 5 and x = -5


Problem 1:

A machine fills Quaker

Oatmeal containers with 32

ounces of oatmeal. After

the containers are filled,

another machine weighs

them. If the container's

weight differs from the

desired 32 ounce weight by

more than 0.5 ounces, the

container is rejected.

Write an equation that can be used to find the heaviest

and lightest acceptable

weights for the Quaker

Oatmeal container. Solve

the equation.


Practice:

Extraneous solution: is a solution of an equation derived from an

original equation that is not a solution.


Absolute value

Inequalities:

Discuss with your teams

What it means for

X is more than 3 units from 0 on the number

Line.

Which provides the same graph as

x < -3 or x > 3

X is less than 3 units from 0 on the number line.

Which also provides the same graph as

-3 < x < 3


Hint: Great”or” than

So…we conclude that

Is equivalent to

Is equivalent to

Or

Hint: Less th”and”



Problem:

Amy is thinking

of two numbers a and b.

The sum of the two

numbers must be within

10 units of zero. If a is

between -100 and 100,

write a compound

inequality that describes

The possible values of b


Closure Activity: Absolute value inequalities

Give every pair of students a set of Activity 1 Cards. Explain that student

pairs will play a game to match an inequality with the graph of its solution

set, the statement describing its solution set, and the corresponding

compound statement. Have pairs shuffle their cards and deal 8 cards each.

In turn, each player places one card on the table. If there is a corresponding

card already on the table, the player places his/her card on top of that card

to create a stack; if not, the player starts a new stack. At the end of the

game, six stacks should have been created. When a student places the fourth

card on any stack, that student collects that stack. The player with the most

stacks wins. Once the game becomes too repetitive with these cards, have

students create their own game cards in the same manner by writing

inequalities, accompanying statements describing the solution sets,

accompanying graphs, and accompanying compound inequalities.

Homework: pages 36-37 #1-64 every 3rd.


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