Download Creating equations and inequalities.

Unit 1, Day 4
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Compare and contrast your slip of paper with
other class mates.
Your slips of paper can be separated into three
distinct groups.
Find all other classmates that you believe should
go into your group.
Once everyone in the class belongs to a group,
decide as a group if you agree that everyone’s
slip belongs in that group.
Once you agree, decide on a label that best
describes all slips of paper in your group. (Keep
it quite!)
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How do I translate “8x=24” into a written
statement?
Eight times a number is 24
This is an equation
How do I translate “fourteen times a number
added to three” into a numerical statement?
14p + 3
This is an expression
How do I translate “2/y > 4w” into a written
statement?
Two divided by a number is greater than four
times another number
This is an inequality
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Word problems offer you a context.
Word problems often give you more
information than necessary
Word problems can usually be simplified into
basic problems (something you already know
how to work with!)
Look for your goal
 Read through the entire problem and get a
goal in mind
 Your goal should be what the problem is
asking you to do
Define your variables
 Look for something we are trying to find (goal)
or do not know
 Decide what you are going to call your
variables
Cross out unimportant information
 Ignore or cross out any added filler in
problems
 Specifically, look for numbers that will not
help you in reaching your goal
Highlight important information
 Look for numbers already given
 Look for math phrases
Write out your equation or inequality
 Use all the information you decided was
important and all of your variables
Check that your answer matches your goal
 Go through the word problem one more time,
phrase by phrase, and make sure everything
in it matches up to how you would read your
numerical problem.
 Then, make sure you have answered what the
problem actually asked.
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Suzanne made a withdrawal of d dollars from
her savings account. Her old balance was
$350, and her new balance is $280. Model
the mathematical statement.
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Model an equation of Suzanne’s old balance
to her new balance
d=number of dollars Suzanne withdrew
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Suzanne made a withdrawal of d dollars from
her savings account. Her old balance was
$350, and her new balance is $280. Model
the mathematical statement.
Suzanne made a withdrawal of d dollars from
her savings account. Her old balance was
$350, and her new balance is $280. Model
the mathematical statement.
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350 – d = 280
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Eleni is x years old. In thirteen years she will
be twenty-four years old. Model her age as a
mathematical statement.
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A large pizza pie with 15 slices is shared
among p students so that each student's
share is 3 slices. Model each student’s share.
Unit 1, Day 5
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Inverse: the direct opposite
The inverse operation “cancels out” an
original operation in the equation or
inequality
Mathematical operations performed on one
side of the equation/inequality must be
performed on the other side to keep the
statement true
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The inverse operation of Addition is…
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The inverse operation of Subtraction is…
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The inverse operation of Multiplication is…
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The inverse operation of Division is…
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The inverse operation of squaring is…
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Subtraction
Addition
Division
Multiplication
Taking a square root
The inverse operation of taking the square
root is…
Squaring
𝑥 + 5 = 25
3
𝑥=6
5
𝑥 2 = 25
𝑥 + 5 − 5 = 25 − 5
3
𝑥 =6÷
5
𝑥2 =
6 5
𝑥= 
1 3
25
𝑥 = 20
𝑥 = 10
𝑥=5
(1)
Take care of any Distributive Property or any other
Multiplication/Division found in the equation.
(2)
Combine Like Terms on the left and right of the equal
sign individually.
Move the variables to one side of the equation and the
constants to the other side (isolate the variable) using
inverse operations.
Get the variable alone (coefficient of 1) by dividing each
side of the equation by the variable’s coefficient.
(3)
(4)
You may have to use the reciprocal of the coefficient if
there is a fraction attached to the variable in the last
step.
1. 9𝑥 + 4 = 31
2. 19 = 2 3𝑤 + 5
3.
−𝑏
7
=9
x=3
9
6
w= =1
1
2
b = -63
4. 17𝑦 − 12 = 12𝑦 + 8
y=4
CHECK YOUR SOLUTIONS!
1. 𝑥 + 5 > 14
2. 3𝑥 ≤ 9
𝑥>9
𝑥 ≤3
3. 15 + 7𝑦 ≥ 36
𝑦≥3
4. 4 − 2𝑥 ≤ 6
5.
𝑋
−4
< −8
CHECK YOUR SOLUTIONS!
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Follow the same rules as solving equations
EXCEPT
When multiplying or dividing by a negative,
be sure to flip your inequality sign.
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A number is divided by 3. Then 14 is added
to the quotient. The result is 33.What is the
original number?
Landon has 37 baseball cards. If 4 cards can
fit on one page, how many pages does
Landon need to buy?
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The square root of a number is subtracted
from the sum of the number and 12. The
result is 42. What is the original number?
Kata has a savings account that contains
$230. She decides to deposit $5 each month
from her monthly earnings for baby-sitting
after school. Write an expression to find how
much money Kata will have in her savings
account after X months. Let X represent the
number of months. Then find out how much
she will have in her account after 1 year.