Chapter 2 Flashcards
Do not divide each side of an equation by a ____ when using the MPOE as it may result in an invalid solution.
Variable
3x=15
Do divide by the 3 NOT the x
When using the MPOE it is usually easier to______on each side if the coefficient of the variable is a fraction.
Multiply
3/4x=12
DO multiply both sides by 4/3
When using the MPOE it is usually easier to______on each side if the coefficient of the variable is an integer.
Divide
-5x=-10
DO divide by -5
When using the MPOE and the numerator of a fraction is a variable just replace it with ____
1
x/4=7 is also 1/4 (x)=7
When dealing with a negative variable replace it with ____ then multiply the it and the otherside by -1
-1* (place non-negative variable here)
For example
- k=7 becomes
- 1*k =7
(-1*-1)*k = 7(-1)
k=-7
Whenever there are parentheses w/ unlike terms inside they cannot be combined.
Use the number ____ to remove the parentheses.
1
8a - (3+2a)
Distribute
8a - 1(3+2a)
Remove Parentheses
8a - 3 - 2a
An equation that has exactly one solution is a called______
A conditional equation
Whenever the variable_____ in a true equation the Solution set is considered all real numberes.
It is indicated as _____.
Disappears
{all real #’s}
When simplifying an equation w/ fractions always multiply ____ ____ ____ ___ ____ by the LCD.
both sides of the equation
An equation w/ both sides exactly the same is called an _______.
The solution to this type of problem is all real numbers and is indicated as _____.
identity
{all real #’s}
What am I?
* One soulution
*{a number}
*x= a number
A Conditional equation
What am I?
* Infinite solutions
*{all real #s}
*a true statement with no variable
such as,
0=0
An Identity (equation)
What am I?
* no soultions
*∅ (null/empty set)
*a false statement with no variable
such as
3=4
A Contradiction
When indicating an ∅ (null/empty set) You never write______.
You simply write_____
{∅}
∅
When solving an applied equation the steps are
RAWSAC
What does the stand for?
Read
Assign the variable
Write the equation
Solve
Articulate the answer
Check
An angle can be measured by a unit called a _____
degree °
A degree is _____ of a complete rotation.
1
-
360°
Two angles whose sum is said to be 90° are called _____, or ______ of each other
Complementary
Complements
An angle that measures 90° is a ______ _____
Right angle
Two angles whose sum is said to be 180° are called _____, or ______ of each other
Supplementary
Supplements
Two integers that differ by one are called ______
Consecutive integers
If
x= the first integer…
What formula is used to solve consecutive integer problems with two consecutive integers?
x+1
1,2,3,4…
If
x= the first integer
What formula is used to solve consecutive integer problems with two consecutive even & odd integers.
x+2
2,4,6,8…
1,3,5,7…
An equation in which
VARIABLES
are used to describe a relationship.
Formula
When two lines intersect they create ____ ___ in the corners.
Vertical Angles
When comparing vertical angles, you set each angle, on a side of the equal sign, to create an ________
equation
Angle 1 (°) = Angle 2 (°)
When comparing supplementary angles add both angles together and make the other side of the equation ______.
180°
Angle 1 (°) + Angle 2 (°) = 180°
When you have several problems that can be solved using the same formula, you can rewrite the formula so that you solve for a ______ _______ every time
Different Variable
A=LW
L=A/W
W=A/L
What is it called when you rewrite the formula so that you solve for a different variable?
Solving for a Specified Variable
or
Solving a Literal Equation
Percents are _____ in which the denominator is always ____-
Ratios
100
In terms of proportions (if B and D ≠0)
A,B,C and D
are called…?
A C
- = -
B D
Terms
In terms of proportions (if B and D ≠0)
B and C are called…?
A C
- = -
B D
Means
In terms of proportions (if B and D ≠0)
A and D are called…?
A C
- = -
B D
Extremes
In terms or ratios and proportions, the product of extremes should equal….
The product of the MEANS.
If
A C
- = -
B D
and the denominators are
≠0 then,
this proportion is equal to what else???
A b
- = -
c D
or
d C
- = -
B a
Changing the proportion
A C
- = -
B D
to
A b
- = -
c D
or
d C
- = -
B a
Is called…?
Swapping
When you set cross products equal to each other,
you are really multiplying each ratio in the proportion by a ____ _____.
Common Denominator
The Formula for a mixture problem
Base x Rate = %
B x R = P
The Formula for an Interest problem
Principal x Rate = Interest
P x R = I
The Formula for money denominations problems
Number x Value of One Item= Total Value
Formula for Distance
d=rt
Formula for Rate
r=d/t
Formula for Time
t=d/r
Square brackets (or filled circles) are used on inequality number lines to display ____
Inclusion
Parentheses (or unfilled circles) are used on inequality number lines to display ____
Exclusion
Interval
A portion of a number line
Interval Notation is a simplified notation that uses parentheses () (unfilled circle) and or brackets [] (filled circle) to describe an interval on a number line.
Interval Notation
This sign denotes going on into forever in the negative direction
-∞
Negative Infinity
This sign denotes going on into forever in the positive direction
∞
Positive Infinity
Anytime the Infinity sign is used in interval notation it is always used with _______.
And is denoted as such…
Parentheses
(-∞∞)
What is this called when
A,B, and C are real numbers
and A ≠0
Ax+B< p=””> <>
Linear inequality in one variable
Addition Property Of Inequlity
if
A< p=””><>
then
A+C < B+C
Inequalities are easier to graph when the variable is on the _____
Left
x>-12
instead of
-12<x><></x>
Multiplication property of inequality
For any real numbers A,B, and C,
C≠0 and is positive
A
Then
AC<bc></bc>
BUT* IF C IS NEGATIVE*
**A>B **
Then
AC<bc></bc>
REMEMBER TO:
___ ___ ____ ____ _____ ___
ONLY
when multiplying or dividing each side by a negative number.
Reverse the direction of the inequality symbol
When you reverse an inquality symbol,
becuase it is either being multiplied or divided by a negative number,
its only done when ______
The number is the numerical coefficient.
-3x<18
-3/4x<12
Not
3x< -18
3/4x< -12
In an ineqaulity the phrase what is the meaning of …
a number IS MORE THAN…
x>#
In an ineqaulity the phrase what is the meaning of …
a number IS LESS THAN…
X<#
In an ineqaulity the phrase what is the meaning of …
a number IS AT LEAST…
X ≥#
In an ineqaulity the phrase what is the meaning of …
a numberI IS AT MOST…
X ≤ #
How to find an number average that is an at least or an at most value?
Avg#1 + Avg#2 + Avg#3 +X
______________________ ≤,≥,<,>The Number Desired
4 (the number of # + the variable)
In applied inequality problems
at least
translates into…
greater than or equal to
In applied inequlity problems
at most
translates into
less than or eqal to
An inequality that says that one number is in between two other numbers is called a ____ _____ ______.
Three-Part Inequality
In general three part inequalities are wrottem sp that the symbols point in the ____ _____
and
both point to the ____ ______
Same direction
Same number
When simplfying three-part inequalties
what is done to one portion of the inequality must be done to the…
other two portions.
When solving three-part inequalities you should still _____ ___ _____ ___ after multiplying or dividing by a negative number.
Reverse the inequality symobol
