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Geoffrey has dimes and quarters in his pocket. The number of dimes is seven less than six times the number of quarters. Let q represent the number of quarters. Write an expression for the number of dimes.

6 q − 7

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Lauren has dimes and nickels in her purse. The number of dimes is eight more than four times the number of nickels. Let n represent the number of nickels. Write an expression for the number of dimes.

4 n + 8

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Key concepts

  • Combine like terms.
    1. Identify like terms.
    2. Rearrange the expression so like terms are together.
    3. Add the coefficients of the like terms

Practice makes perfect

Evaluate Algebraic Expressions

In the following exercises, evaluate the expression for the given value.

x 2 + 3 x 7 when x = 4

21

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x 2 + 5 x 8 when x = 6

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2 x + 4 y 5 when x = 7 , y = 8

41

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6 x + 3 y 9 when x = 6 , y = 9

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( x y ) 2 when x = 10 , y = 7

9

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( x + y ) 2 when x = 6 , y = 9

225

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a 2 + b 2 when a = 3 , b = 8

73

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r 2 s 2 when r = 12 , s = 5

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2 l + 2 w when l = 15 , w = 12

54

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2 l + 2 w when l = 18 , w = 14

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Identify Terms, Coefficients, and Like Terms

In the following exercises, list the terms in the given expression.

15 x 2 + 6 x + 2

15 x 2 , 6 x , 2

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10 y 3 + y + 2

10 y 3 , y , 2

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In the following exercises, identify the coefficient of the given term.

In the following exercises, identify all sets of like terms.

x 3 , 8 x , 14 , 8 y , 5 , 8 x 3

x 3 , 8 x 3 and 14, 5

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6 z , 3 w 2 , 1 , 6 z 2 , 4 z , w 2

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9 a , a 2 , 16 a b , 16 b 2 , 4 a b , 9 b 2

16 ab and 4 ab ; 16 b 2 and 9 b 2

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3 , 25 r 2 , 10 s , 10 r , 4 r 2 , 3 s

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Simplify Expressions by Combining Like Terms

In the following exercises, simplify the given expression by combining like terms.

7 u + 2 + 3 u + 1

10 u + 3

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7 p + 6 + 5 p + 4

12 p + 10

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10 a + 7 + 5 a 2 + 7 a 4


22 a + 1

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7 c + 4 + 6 c 3 + 9 c 1

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3 x 2 + 12 x + 11 + 14 x 2 + 8 x + 5

17 x 2 + 20 x + 16

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5 b 2 + 9 b + 10 + 2 b 2 + 3 b 4

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Translate English Phrases into Algebraic Expressions

In the following exercises, translate the given word phrase into an algebraic expression.

The sum of 8 and 12

8 + 12

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The difference of 14 and 9

14 − 9

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The product of 9 and 7

9 ⋅ 7

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The quotient of 36 and 9

36 ÷ 9

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The quotient of 42 and 7

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The difference of x and 4

x − 4

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The product of 6 and y

6 y

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The sum of 8 x and 3 x

8 x + 3 x

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The quotient of y and 3

y 3

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Eight times the difference of y and nine

8 ( y − 9)

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Seven times the difference of y and one

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Five times the sum of x and y

5 ( x + y )

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Nine times five less than twice x

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In the following exercises, write an algebraic expression.

Adele bought a skirt and a blouse. The skirt cost $15 more than the blouse. Let b represent the cost of the blouse. Write an expression for the cost of the skirt.

b + 15

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Eric has rock and classical CDs in his car. The number of rock CDs is 3 more than the number of classical CDs. Let c represent the number of classical CDs. Write an expression for the number of rock CDs.

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The number of girls in a second-grade class is 4 less than the number of boys. Let b represent the number of boys. Write an expression for the number of girls.

b − 4

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Marcella has 6 fewer male cousins than female cousins. Let f represent the number of female cousins. Write an expression for the number of boy cousins.

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Greg has nickels and pennies in his pocket. The number of pennies is seven less than twice the number of nickels. Let n represent the number of nickels. Write an expression for the number of pennies.

2 n − 7

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Jeannette has $5 and $10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives.

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Everyday math

In the following exercises, use algebraic expressions to solve the problem.

Car insurance Justin’s car insurance has a $750 deductible per incident. This means that he pays $750 and his insurance company will pay all costs beyond $750. If Justin files a claim for $2,100, how much will he pay, and how much will his insurance company pay?

He will pay $750. His insurance company will pay $1350.

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Home insurance Pam and Armando’s home insurance has a $2,500 deductible per incident. This means that they pay $2,500 and their insurance company will pay all costs beyond $2,500. If Pam and Armando file a claim for $19,400, how much will they pay, and how much will their insurance company pay?

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Writing exercises

Explain why “the sum of x and y ” is the same as “the sum of y and x ,” but “the difference of x and y ” is not the same as “the difference of y and x .” Try substituting two random numbers for x and y to help you explain.

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Explain the difference between “4 times the sum of x and y and “the sum of 4 times x and y .”

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Self check

After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

.

After reviewing this checklist, what will you do to become confident for all objectives?

Questions & Answers

Do somebody tell me a best nano engineering book for beginners?
s. Reply
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
AMJAD
what is system testing
AMJAD
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Berger describes sociologists as concerned with
Mueller Reply
What is the expressiin for seven less than four times the number of nickels
Leonardo Reply
How do i figure this problem out.
how do you translate this in Algebraic Expressions
linda Reply
why surface tension is zero at critical temperature
Shanjida
I think if critical temperature denote high temperature then a liquid stats boils that time the water stats to evaporate so some moles of h2o to up and due to high temp the bonding break they have low density so it can be a reason
s.
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
Practice Key Terms 4

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Source:  OpenStax, Prealgebra. OpenStax CNX. Jul 15, 2016 Download for free at http://legacy.cnx.org/content/col11756/1.9
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