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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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?
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
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
Extraneous solution: is a solution of an equation derived from an
original equation that is not a solution.
Discuss with your teams
What it means for
X is more than 3 units from 0 on the number
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
So…we conclude that
Is equivalent to
Is equivalent to
Hint: Less th”and”
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
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.