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Solve Equations Using the Subtraction and Addition Properties of Equality

In the following exercises, determine whether the given value is a solution to the equation.

Is y = 1 3 a solution of 4 y + 2 = 10 y ?

yes

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Is x = 3 4 a solution of 5 x + 3 = 9 x ?

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Is u = 1 2 a solution of 8 u 1 = 6 u ?

no

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Is v = 1 3 a solution of 9 v 2 = 3 v ?

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In the following exercises, solve each equation.

p + 2.4 = −9.3

p = −11.7

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x 15 = −42

x = −27

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q + 3 4 = 1 2

q = 1 4

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y 3 4 = 3 5

y = 27 20

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Solve Equations that Need to be Simplified

In the following exercises, solve each equation.

9 x + 5 8 x + 14 = 20

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6 x + 8 5 x + 16 = 32

8

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−6 x 11 + 7 x 5 = −16

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−8 n 17 + 9 n 4 = −41

−20

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3 ( y 5 ) 2 y = −7

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4 ( y 2 ) 3 y = −6

2

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8 ( u + 1.5 ) 7 u = 4.9

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5 ( w + 2.2 ) 4 w = 9.3

1.7

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−5 ( y 2 ) + 6 y = −7 + 4

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−8 ( x 1 ) + 9 x = −3 + 9

−2

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3 ( 5 n 1 ) 14 n + 9 = 1 2

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2 ( 8 m + 3 ) 15 m 4 = 3 5

−4

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( j + 2 ) + 2 j 1 = 5

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( k + 7 ) + 2 k + 8 = 7

6

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6 a 5 ( a 2 ) + 9 = −11

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8 c 7 ( c 3 ) + 4 = −16

−41

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8 ( 4 x + 5 ) 5 ( 6 x ) x = 53

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6 ( 9 y 1 ) 10 ( 5 y ) 3 y = 22

28

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Translate to an Equation and Solve

In the following exercises, translate to an equation and then solve.

Five more than x is equal to 21 .

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The sum of x and −5 is 33 .

x + (−5) = 33; x = 38

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Ten less than m is −14 .

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Three less than y is −19 .

y − 3 = −19; y = −16

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The sum of y and −3 is 40 .

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Eight more than p is equal to 52 .

p + 8 = 52; p = 44

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The difference of 9 x and 8 x is 17 .

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The difference of 5 c and 4 c is 60 .

5 c − 4 c = 60; 60

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The difference of n and 1 6 is 1 2 .

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The difference of f and 1 3 is 1 12 .

f 1 3 = 1 12 ; 5 12

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The sum of −4 n and 5 n is −32 .

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The sum of −9 m and 10 m is −25 .

−9 m + 10 m = −25; m = −25

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Translate and Solve Applications

In the following exercises, translate into an equation and solve.

Pilar drove from home to school and then to her aunt’s house, a total of 18 miles. The distance from Pilar’s house to school is 7 miles. What is the distance from school to her aunt’s house?

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Jeff read a total of 54 pages in his English and Psychology textbooks. He read 41 pages in his English textbook. How many pages did he read in his Psychology textbook?

Let p equal the number of pages read in the Psychology book 41 + p = 54. Jeff read pages in his Psychology book.

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Pablo’s father is 3 years older than his mother. Pablo’s mother is 42 years old. How old is his father?

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Eva’s daughter is 5 years younger than her son. Eva’s son is 12 years old. How old is her daughter?

Let d equal the daughter’s age. d = 12 − 5. Eva’s daughter’s age is 7 years old.

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Allie weighs 8 pounds less than her twin sister Lorrie. Allie weighs 124 pounds. How much does Lorrie weigh?

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For a family birthday dinner, Celeste bought a turkey that weighed 5 pounds less than the one she bought for Thanksgiving. The birthday dinner turkey weighed 16 pounds. How much did the Thanksgiving turkey weigh?

21 pounds

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The nurse reported that Tricia’s daughter had gained 4.2 pounds since her last checkup and now weighs 31.6 pounds. How much did Tricia’s daughter weigh at her last checkup?

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Connor’s temperature was 0.7 degrees higher this morning than it had been last night. His temperature this morning was 101.2 degrees. What was his temperature last night?

100.5 degrees

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Melissa’s math book cost $22.85 less than her art book cost. Her math book cost $93.75 . How much did her art book cost?

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Ron’s paycheck this week was $17.43 less than his paycheck last week. His paycheck this week was $103.76 . How much was Ron’s paycheck last week?

$121.19

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Everyday math

Baking Kelsey needs 2 3 cup of sugar for the cookie recipe she wants to make. She only has 1 4 cup of sugar and will borrow the rest from her neighbor. Let s equal the amount of sugar she will borrow. Solve the equation 1 4 + s = 2 3 to find the amount of sugar she should ask to borrow.

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Construction Miguel wants to drill a hole for a 5 8 -inch screw. The screw should be 1 12 inch larger than the hole. Let d equal the size of the hole he should drill. Solve the equation d + 1 12 = 5 8 to see what size the hole should be.

d = 13 24

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Writing exercises

Is −18 a solution to the equation 3 x = 16 5 x ? How do you know?

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Write a word sentence that translates the equation y 18 = 41 and then make up an application that uses this equation in its solution.

Answers will vary.

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Self check

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

.

If most of your checks were:

…confidently. Congratulations! You have achieved the objectives in this section. Reflect on the study skills you used so that you can continue to use them. What did you do to become confident of your ability to do these things? Be specific.

…with some help. This must be addressed quickly because topics you do not master become potholes in your road to success. In math, every topic builds upon previous work. It is important to make sure you have a strong foundation before you move on. Who can you ask for help? Your fellow classmates and instructor are good resources. Is there a place on campus where math tutors are available? Can your study skills be improved?

…no—I don’t get it! This is a warning sign and you must not ignore it. You should get help right away or you will quickly be overwhelmed. See your instructor as soon as you can to discuss your situation. Together you can come up with a plan to get you the help you need.

Questions & Answers

anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
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
Do you know which machine is used to that process?
s.
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
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
Good
Berger describes sociologists as concerned with
Mueller Reply
A soccer field is a rectangle 130 meters wide and 110 meters long. The coach asks players to run from one corner to the other corner diagonally across. What is that distance, to the nearest tenths place.
Kimberly Reply
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.
August 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 1

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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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