<< 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

what does preconceived mean
sammie Reply
physiological Psychology
Nwosu Reply
How can I develope my cognitive domain
Amanyire Reply
why is communication effective
Dakolo Reply
Communication is effective because it allows individuals to share ideas, thoughts, and information with others.
effective communication can lead to improved outcomes in various settings, including personal relationships, business environments, and educational settings. By communicating effectively, individuals can negotiate effectively, solve problems collaboratively, and work towards common goals.
it starts up serve and return practice/assessments.it helps find voice talking therapy also assessments through relaxed conversation.
miss
Every time someone flushes a toilet in the apartment building, the person begins to jumb back automatically after hearing the flush, before the water temperature changes. Identify the types of learning, if it is classical conditioning identify the NS, UCS, CS and CR. If it is operant conditioning, identify the type of consequence positive reinforcement, negative reinforcement or punishment
Wekolamo Reply
please i need answer
Wekolamo
because it helps many people around the world to understand how to interact with other people and understand them well, for example at work (job).
Manix Reply
Agreed 👍 There are many parts of our brains and behaviors, we really need to get to know. Blessings for everyone and happy Sunday!
ARC
A child is a member of community not society elucidate ?
JESSY Reply
Isn't practices worldwide, be it psychology, be it science. isn't much just a false belief of control over something the mind cannot truly comprehend?
Simon Reply
compare and contrast skinner's perspective on personality development on freud
namakula Reply
Skinner skipped the whole unconscious phenomenon and rather emphasized on classical conditioning
war
explain how nature and nurture affect the development and later the productivity of an individual.
Amesalu Reply
nature is an hereditary factor while nurture is an environmental factor which constitute an individual personality. so if an individual's parent has a deviant behavior and was also brought up in an deviant environment, observation of the behavior and the inborn trait we make the individual deviant.
Samuel
I am taking this course because I am hoping that I could somehow learn more about my chosen field of interest and due to the fact that being a PsyD really ignites my passion as an individual the more I hope to learn about developing and literally explore the complexity of my critical thinking skills
Zyryn Reply
good👍
Jonathan
and having a good philosophy of the world is like a sandwich and a peanut butter 👍
Jonathan
generally amnesi how long yrs memory loss
Kelu Reply
interpersonal relationships
Abdulfatai Reply
What would be the best educational aid(s) for gifted kids/savants?
Heidi Reply
treat them normal, if they want help then give them. that will make everyone happy
Saurabh
What are the treatment for autism?
Magret Reply
hello. autism is a umbrella term. autistic kids have different disorder overlapping. for example. a kid may show symptoms of ADHD and also learning disabilities. before treatment please make sure the kid doesn't have physical disabilities like hearing..vision..speech problem. sometimes these
Jharna
continue.. sometimes due to these physical problems..the diagnosis may be misdiagnosed. treatment for autism. well it depends on the severity. since autistic kids have problems in communicating and adopting to the environment.. it's best to expose the child in situations where the child
Jharna
child interact with other kids under doc supervision. play therapy. speech therapy. Engaging in different activities that activate most parts of the brain.. like drawing..painting. matching color board game. string and beads game. the more you interact with the child the more effective
Jharna
results you'll get.. please consult a therapist to know what suits best on your child. and last as a parent. I know sometimes it's overwhelming to guide a special kid. but trust the process and be strong and patient as a parent.
Jharna
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