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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

Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
hi
Loga
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
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
what is hormones?
Wellington
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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