<< Chapter < Page Chapter >> Page >

Equality and inequality symbols

a = b a and b are equal a > b a is strictly greater than b a < b a is strictly less than b

Some variations of these symbols include

a b a is not equal to b a b a is greater than or equal to b a b a is less than or equal to b

The last five of the above symbols are inequality symbols. We can negate (change to the opposite) any of the above statements by drawing a line through the relation symbol (as in a b ), as shown below:

a is not greater than b can be expressed as either

a > b or a b.

a is not less b than can be expressed as either

a < b or a b.

a < b and a b both indicate that a is less than b .

Grouping symbols

Grouping symbols are used to indicate that a particular collection of numbers and meaningful operations are to be grouped together and considered as one number. The grouping symbols commonly used in algebra are

Parentheses: ( ) Brackets: [ ] Braces: { } Bar: ¯

In a computation in which more than one operation is involved, grouping symbols help tell us which operations to perform first. If possible, we perform operations inside grouping symbols first.

Sample set b

( 4 + 17 ) 6 = 21 6 = 15

Got questions? Get instant answers now!

8 ( 3 + 6 ) = 8 ( 9 ) = 72

Got questions? Get instant answers now!

5 [ 8 + ( 10 4 ) ] = 5 [ 8 + 6 ] = 5 [ 14 ] = 70

Got questions? Get instant answers now!

2 { 3 [ 4 ( 17 11 ) ] } = 2 { 3 [ 4 ( 6 ) ] } = 2 { 3 [ 24 ] } = 2 { 72 } = 144

Got questions? Get instant answers now!

9 ( 5 + 1 ) 24 + 3 .

The fraction bar separates the two groups of numbers 9 ( 5 + 1 ) and 24 + 3 . Perform the operations in the numerator and denominator separately.

9 ( 5 + 1 ) 24 + 3 = 9 ( 6 ) 24 + 3 = 54 24 + 3 = 54 27 = 2

Got questions? Get instant answers now!

Practice set b

Use the grouping symbols to help perform the following operations.

6 { 2 [ 2 ( 10 9 ) ] }

24

Got questions? Get instant answers now!

The following examples show how to use algebraic notation to write each expression.

9 minus y becomes 9 y

Got questions? Get instant answers now!

7 times ( x + y ) becomes 7 ( x + y )

Got questions? Get instant answers now!

4 divided by 3, times z becomes ( 4 3 ) z

Got questions? Get instant answers now!

( a b ) times ( b a ) divided by (2 times a ) becomes ( a b ) ( b a ) 2 a

Got questions? Get instant answers now!

Introduce a variable ( any letter will do but here we’ll let x represent the number) and use appropriate algebraic symbols to write the statement: A number plus 4 is strictly greater than 6. The answer is x + 4 > 6 .

Got questions? Get instant answers now!

The order of operations

Suppose we wish to find the value of 16 + 4 9 . We could

  1. add 16 and 4, then multiply this sum by 9.
    16 + 4 9 = 20 9 = 180
  2. multiply 4 and 9, then add 16 to this product.
    16 + 4 9 = 16 + 36 = 52

We now have two values for one number. To determine the correct value we must use the standard order of operations .

    Order of operations

  1. Perform all operations inside grouping symbols, beginning with the innermost set.
  2. Perform all multiplications and divisions, as you come to them, moving left-to-right.
  3. Perform all additions and subtractions, as you come to them, moving left-to-right.

As we proceed in our study of algebra, we will come upon another operation, exponentiation, that will need to be inserted before multiplication and division. (See Section [link] .)

Sample set c

USe the order of operations to find the value of each number.

16 + 4 9 Multiply first . = 16 + 36 Now add . = 52

Got questions? Get instant answers now!

( 27 8 ) + 7 ( 6 + 12 ) Combine within parentheses . = 19 + 7 ( 18 ) Multiply . = 19 + 126 Now add . = 145

Got questions? Get instant answers now!

8 + 2 [ 4 + 3 ( 6 1 ) ] Begin with the innermost set of grouping symbols , ( ) . = 8 + 2 [ 4 + 3 ( 5 ) ] Now work within the next set of grouping symbols , [ ] . = 8 + 2 [ 4 + 15 ] = 8 + 2 [ 19 ] = 8 + 38 = 46

Got questions? Get instant answers now!

6 + 4 [ 2 + 3 ( 19 17 ) ] 18 2 [ 2 ( 3 ) + 2 ] = 6 + 4 [ 2 + 3 ( 2 ) ] 18 2 [ 6 + 2 ] = 6 + 4 [ 2 + 6 ] 18 2 [ 8 ] = 6 + 4 [ 8 ] 18 16 = 6 + 32 2 = 38 2 = 19

Got questions? Get instant answers now!

Practice set c

Use the order of operations to find each value.

2 + 3 ( 18 5 2 )

26

Got questions? Get instant answers now!

4 + 3 [ 2 + 3 ( 1 + 8 ÷ 4 ) ]

37

Got questions? Get instant answers now!

19 + 2 { 5 + 2 [ 18 + 6 ( 4 + 1 ) ] } 5 6 3 ( 5 ) 2

17

Got questions? Get instant answers now!

Exercises

For the following problems, use the order of operations to find each value.

6 ( 4 + 1 ) ÷ ( 16 ÷ 8 ) 15

Got questions? Get instant answers now!

6 ( 4 1 ) + 8 ( 3 + 7 ) 20

78

Got questions? Get instant answers now!

( 8 ) ( 5 ) + 2 ( 14 ) + ( 1 ) ( 10 )

Got questions? Get instant answers now!

61 22 + 4 [ 3 ( 10 ) + 11 ]

203

Got questions? Get instant answers now!

( 1 + 16 3 ) 7 + 5 ( 12 )

Got questions? Get instant answers now!

8 ( 6 + 20 ) 8 + 3 ( 6 + 16 ) 22

29

Got questions? Get instant answers now!

( 300 25 ) ÷ ( 6 3 )

91 2 3

Got questions? Get instant answers now!

4 3 + 8 28 ( 3 + 17 ) + 11 ( 6 )

Got questions? Get instant answers now!

2 { ( 7 + 7 ) + 6 [ 4 ( 8 + 2 ) ] }

508

Got questions? Get instant answers now!

0 + 10 ( 0 ) + 15 [ 4 ( 3 ) + 1 ]

Got questions? Get instant answers now!

( 4 + 7 ) ( 8 3 )

55

Got questions? Get instant answers now!

( 10 + 5 ) ( 10 + 5 ) 4 ( 60 4 )

Got questions? Get instant answers now!

( 5 12 1 4 ) + ( 1 6 + 2 3 )

1

Got questions? Get instant answers now!

4 ( 3 5 8 15 ) + 9 ( 1 3 + 1 4 )

Got questions? Get instant answers now!

0 5 + 0 1 + 0 [ 2 + 4 ( 0 ) ]

0

Got questions? Get instant answers now!

0 9 + 4 0 ÷ 7 + 0 [ 2 ( 2 2 ) ]

Got questions? Get instant answers now!

For the following problems, state whether the given statements are the same or different.

x y and x > y

different

Got questions? Get instant answers now!

Represent the product of 3 and x five different ways.

Got questions? Get instant answers now!

Represent the sum of a and b two different ways.

a + b , b + a

Got questions? Get instant answers now!

For the following problems, rewrite each phrase using algebraic notation.

( x + b ) times ( x + 7 )

( x + b ) ( x + 7 )

Got questions? Get instant answers now!

x divided by (7 times b )

x 7 b

Got questions? Get instant answers now!

( a + b ) divided by ( a + 4 )

Got questions? Get instant answers now!

For the following problems, introduce a variable (any letter will do) and use appropriate algebraic symbols towrite the given statement.

A number minus eight equals seventeen.

x 8 = 17

Got questions? Get instant answers now!

Five times a number, minus one, equals zero.

Got questions? Get instant answers now!

A number divided by six is greater than or equal to forty-four.

x 6 44

Got questions? Get instant answers now!

Sixteen minus twice a number equals five.

Got questions? Get instant answers now!

Determine whether the statements for the following problems are true or false.

6 4 ( 4 ) ( 1 ) 10

true

Got questions? Get instant answers now!

5 ( 4 + 2 10 ) 110

Got questions? Get instant answers now!

8 6 48 0

true

Got questions? Get instant answers now!

2 [ 6 ( 1 + 4 ) 8 ] > 3 ( 11 + 6 )

false

Got questions? Get instant answers now!

6 [ 4 + 8 + 3 ( 26 - 15 ) ] Is not less than or equal to 3 [ 7 ( 10 - 4 ) ]

Got questions? Get instant answers now!

The number of different ways 5 people can be arranged in a row is 5 4 3 2 1 . How many ways is this?

120

Got questions? Get instant answers now!

A box contains 10 computer chips. Three chips are to be chosen at random. The number of ways this can be done is

1 0 9 8 7 6 5 4 3 2 1 3 2 1 7 6 5 4 3 2 1

How many ways is this?

Got questions? Get instant answers now!

The probability of obtaining four of a kind in a five-card poker hand is

13 48 ( 52 51 50 49 48 ) ÷ ( 5 4 3 2 1 )

What is this probability?

0.00024 , or 1 4165

Got questions? Get instant answers now!

Three people are on an elevator in a five story building. If each person randomly selects a floor on which to get off, the probability that at least two people get off on the same floor is

1 5 4 3 5 5 5

What is this probability?

Got questions? Get instant answers now!

Questions & Answers

it is the relatively stable flow of income
Chidubem Reply
what is circular flow of income
Divine Reply
branches of macroeconomics
SHEDRACK Reply
what is Flexible exchang rate?
poudel Reply
is gdp a reliable measurement of wealth
Atega Reply
introduction to econometrics
Husseini Reply
Hi
mostafa
hi
LEMLEM
hello
Sammol
hi
Mahesh
bi
Ruqayat
hi
Ruqayat
Hi fellas
Nyawa
hey
Sammol
hi
God
hello
Jahara
Good morning
Jorge
hi
abubakar
hi
Nmesoma
hi
Mahesh
Hi
Tom
Why is unemployment rate never zero at full employment?
Priyanka Reply
bcoz of existence of frictional unemployment in our economy.
Umashankar
what is flexible exchang rate?
poudel
due to existence of the pple with disabilities
Abdulraufu
the demand of a good rises, causing the demand for another good to fall
Rushawn Reply
is it possible to leave every good at the same level
Joseph
I don't think so. because check it, if the demand for chicken increases, people will no longer consume fish like they used to causing a fall in the demand for fish
Anuolu
is not really possible to let the value of a goods to be same at the same time.....
Salome
Suppose the inflation rate is 6%, does it mean that all the goods you purchase will cost 6% more than previous year? Provide with reasoning.
Geetha Reply
Not necessarily. To measure the inflation rate economists normally use an averaged price index of a basket of certain goods. So if you purchase goods included in the basket, you will notice that you pay 6% more, otherwise not necessarily.
Waeth
discus major problems of macroeconomics
Alii Reply
what is the problem of macroeconomics
Yoal
Economic growth Stable prices and low unemployment
Ephraim
explain inflationcause and itis degre
Miresa Reply
what is inflation
Getu
increase in general price levels
WEETO
Good day How do I calculate this question: C= 100+5yd G= 2000 T= 2000 I(planned)=200. Suppose the actual output is 3000. What is the level of planned expenditures at this level of output?
Chisomo Reply
how to calculate actual output?
Chisomo
how to calculate the equilibrium income
Beshir
Criteria for determining money supply
Thapase Reply
who we can define macroeconomics in one line
Muhammad
Aggregate demand
Mohammed
C=k100 +9y and i=k50.calculate the equilibrium level of output
Mercy Reply
Hi
Isiaka
Hi
Geli
hy
Man
👋
Bahunda
hy how are you?
Man
ys
Amisha
how are you guys
Sekou
f9 guys
Amisha
how are you guys
Sekou
ys am also fine
Amisha
fine and you guys
Geli
from Nepal
Amisha
nawalparasi district from belatari
Amisha
nd u
Amisha
I am Camara from Guinea west Africa... happy to meet you guys here
Sekou
ma management ho
Amisha
ahile becheclor ho
Amisha
hjr ktm bta ho ani k kaam grnu hunxa tw
Amisha
belatari
Amisha
1st year ho
Amisha
nd u
Amisha
ahh
Amisha
kaha biratnagar
Amisha
ys
Amisha
kina k vo
Amisha
money as unit of account means what?
Kalombe
A unit of account is something that can be used to value goods and services and make calculations
Jim
all of you please speak in English I can't understand you're language
Muhammad
I want to know how can we define macroeconomics in one line
Muhammad
it must be .9 or 0.9 no Mpc is greater than 1 Y=100+.9Y+50 Y-.9Y=150 0.1Y/0.1=150/0.1 Y=1500
Kalombe
Mercy is it clear?😋
Kalombe
hi can someone help me on this question If a negative shocks shifts the IS curve to the left, what type of policy do you suggest so as to stabilize the level of output? discuss your answer using appropriate graph.
Galge Reply
if interest rate is increased this will will reduce the level of income shifting the curve to the left ◀️
Kalombe
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Elementary algebra. OpenStax CNX. May 08, 2009 Download for free at http://cnx.org/content/col10614/1.3
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Elementary algebra' conversation and receive update notifications?

Ask