Brainscape's Knowledge GenomeTM

Browse over 1 million classes created by top students, professors, publishers, and experts.


See full index

Algebra 1 > Chapter 2 > Flashcards

Chapter 2 Flashcards

1
Q

Do not divide each side of an equation by a ____ when using the MPOE as it may result in an invalid solution.

A

Variable

3x=15

Do divide by the 3 NOT the x

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

When using the MPOE it is usually easier to______on each side if the coefficient of the variable is a fraction.

A

Multiply

3/4x=12

DO multiply both sides by 4/3

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

When using the MPOE it is usually easier to______on each side if the coefficient of the variable is an integer.

A

Divide

-5x=-10

DO divide by -5

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

When using the MPOE and the numerator of a fraction is a variable just replace it with ____

A

1

x/4=7 is also 1/4 (x)=7

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

When dealing with a negative variable replace it with ____ then multiply the it and the otherside by -1

A

-1* (place non-negative variable here)

For example

  • k=7 becomes
  • 1*k =7

(-1*-1)*k = 7(-1)

k=-7

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

Whenever there are parentheses w/ unlike terms inside they cannot be combined.

Use the number ____ to remove the parentheses.

A

1

8a - (3+2a)

Distribute

8a - 1(3+2a)

Remove Parentheses

8a - 3 - 2a

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

An equation that has exactly one solution is a called______

A

A conditional equation

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

Whenever the variable_____ in a true equation the Solution set is considered all real numberes.

It is indicated as _____.

A

Disappears

{all real #’s}

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

When simplifying an equation w/ fractions always multiply ____ ____ ____ ___ ____ by the LCD.

A

both sides of the equation

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

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 _____.

A

identity

{all real #’s}

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

What am I?

* One soulution

*{a number}

*x= a number

A

A Conditional equation

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

What am I?

* Infinite solutions

*{all real #s}

*a true statement with no variable

such as,

0=0

A

An Identity (equation)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

What am I?

* no soultions

*∅ (null/empty set)

*a false statement with no variable

such as

3=4

A

A Contradiction

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

When indicating an ∅ (null/empty set) You never write______.

You simply write_____

A

{∅}

∅

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

When solving an applied equation the steps are

RAWSAC

What does the stand for?

A

Read

Assign the variable

Write the equation

Solve

Articulate the answer

Check

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

An angle can be measured by a unit called a _____

A

degree °

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
17
Q

A degree is _____ of a complete rotation.

A

1

-

360°

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
18
Q

Two angles whose sum is said to be 90° are called _____, or ______ of each other

A

Complementary

Complements

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
19
Q

An angle that measures 90° is a ______ _____

A

Right angle

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
20
Q

Two angles whose sum is said to be 180° are called _____, or ______ of each other

A

Supplementary

Supplements

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
21
Q

Two integers that differ by one are called ______

A

Consecutive integers

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
22
Q

If

x= the first integer…

What formula is used to solve consecutive integer problems with two consecutive integers?

A

x+1

1,2,3,4…

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
23
Q

If

x= the first integer

What formula is used to solve consecutive integer problems with two consecutive even & odd integers.

A

x+2

2,4,6,8…

1,3,5,7…

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
24
Q

An equation in which

VARIABLES

are used to describe a relationship.

A

Formula

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
25
Q

When two lines intersect they create ____ ___ in the corners.

A

Vertical Angles

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
26
Q

When comparing vertical angles, you set each angle, on a side of the equal sign, to create an ________

A

equation

Angle 1 (°) = Angle 2 (°)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
27
Q

When comparing supplementary angles add both angles together and make the other side of the equation ______.

A

180°

Angle 1 (°) + Angle 2 (°) = 180°

28
Q

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

A

Different Variable

A=LW

L=A/W

W=A/L

29
Q

What is it called when you rewrite the formula so that you solve for a different variable?

A

Solving for a Specified Variable

or

Solving a Literal Equation

30
Q

Percents are _____ in which the denominator is always ____-

A

Ratios

100

31
Q

In terms of proportions (if B and D ≠0)

A,B,C and D

are called…?

A C

  • = -

B D

A

Terms

32
Q

In terms of proportions (if B and D ≠0)

B and C are called…?

A C

  • = -

B D

A

Means

33
Q

In terms of proportions (if B and D ≠0)

A and D are called…?

A C

  • = -

B D

A

Extremes

34
Q

In terms or ratios and proportions, the product of extremes should equal….

A

The product of the MEANS.

35
Q

If

A C

  • = -

B D

and the denominators are

≠0 then,

this proportion is equal to what else???

A

A b

  • = -

c D

or

d C

  • = -

B a

36
Q

Changing the proportion

A C

  • = -

B D

to

A b

  • = -

c D

or

d C

  • = -

B a

Is called…?

A

Swapping

37
Q

When you set cross products equal to each other,

you are really multiplying each ratio in the proportion by a ____ _____.

A

Common Denominator

38
Q

The Formula for a mixture problem

A

Base x Rate = %

B x R = P

39
Q

The Formula for an Interest problem

A

Principal x Rate = Interest

P x R = I

40
Q

The Formula for money denominations problems

A

Number x Value of One Item= Total Value

41
Q

Formula for Distance

A

d=rt

42
Q

Formula for Rate

A

r=d/t

43
Q

Formula for Time

A

t=d/r

44
Q

Square brackets (or filled circles) are used on inequality number lines to display ____

A

Inclusion

45
Q

Parentheses (or unfilled circles) are used on inequality number lines to display ____

A

Exclusion

46
Q

Interval

A

A portion of a number line

47
Q

Interval Notation is a simplified notation that uses parentheses () (unfilled circle) and or brackets [] (filled circle) to describe an interval on a number line.

A

Interval Notation

48
Q

This sign denotes going on into forever in the negative direction

-∞

A

Negative Infinity

49
Q

This sign denotes going on into forever in the positive direction

∞

A

Positive Infinity

50
Q

Anytime the Infinity sign is used in interval notation it is always used with _______.

And is denoted as such…

A

Parentheses

(-∞∞)

51
Q

What is this called when

A,B, and C are real numbers

and A ≠0

Ax+B< p=””> <>

A

Linear inequality in one variable

52
Q

Addition Property Of Inequlity

A

if

A< p=””><>

then

A+C < B+C

53
Q

Inequalities are easier to graph when the variable is on the _____

A

Left

x>-12

instead of

-12<x>&lt;&gt;</x>

54
Q

Multiplication property of inequality

A

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>

55
Q

REMEMBER TO:

___ ___ ____ ____ _____ ___

ONLY

when multiplying or dividing each side by a negative number.

A

Reverse the direction of the inequality symbol

56
Q

When you reverse an inquality symbol,

becuase it is either being multiplied or divided by a negative number,

its only done when ______

A

The number is the numerical coefficient.

-3x<18

-3/4x<12

Not

3x< -18

3/4x< -12

57
Q

In an ineqaulity the phrase what is the meaning of …

a number IS MORE THAN…

A

x>#

58
Q

In an ineqaulity the phrase what is the meaning of …

a number IS LESS THAN…

A

X<#

59
Q

In an ineqaulity the phrase what is the meaning of …

a number IS AT LEAST…

A

X ≥#

60
Q

In an ineqaulity the phrase what is the meaning of …

a numberI IS AT MOST…

A

X ≤ #

61
Q

How to find an number average that is an at least or an at most value?

A

Avg#1 + Avg#2 + Avg#3 +X

______________________ ≤,≥,<,>The Number Desired

4 (the number of # + the variable)

62
Q

In applied inequality problems

at least

translates into…

A

greater than or equal to

63
Q

In applied inequlity problems

at most

translates into

A

less than or eqal to

64
Q

An inequality that says that one number is in between two other numbers is called a ____ _____ ______.

A

Three-Part Inequality

65
Q

In general three part inequalities are wrottem sp that the symbols point in the ____ _____

and

both point to the ____ ______

A

Same direction

Same number

66
Q

When simplfying three-part inequalties

what is done to one portion of the inequality must be done to the…

A

other two portions.

67
Q

When solving three-part inequalities you should still _____ ___ _____ ___ after multiplying or dividing by a negative number.

A

Reverse the inequality symobol

Algebra 1 (8 decks)

Brainscape helps you reach your goals faster, through stronger study habits.
© 2024 Bold Learning Solutions. Terms and Conditions