<< Chapter < Page Chapter >> Page >

Solve: 8 x + 9 x 5 x = −3 + 15 .

Solution

Start by combining like terms to simplify each side.

.
Combine like terms. .
Divide both sides by 12 to isolate x. .
Simplify. .
Check your answer. Let x = 1
.
.
.
.
Got questions? Get instant answers now!
Got questions? Get instant answers now!

Solve: 7 x + 6 x 4 x = −8 + 26 .

x = 2

Got questions? Get instant answers now!

Solve: 11 n 3 n 6 n = 7 17 .

n = −5

Got questions? Get instant answers now!

Solve: 11 20 = 17 y 8 y 6 y .

Solution

Simplify each side by combining like terms.

.
Simplify each side. .
Divide both sides by 3 to isolate y. .
Simplify. .
Check your answer. Let y = −3
.
.
.
.

Notice that the variable ended up on the right side of the equal sign when we solved the equation. You may prefer to take one more step to write the solution with the variable on the left side of the equal sign.

Got questions? Get instant answers now!
Got questions? Get instant answers now!

Solve: 18 27 = 15 c 9 c 3 c .

c = −3

Got questions? Get instant answers now!

Solve: 18 22 = 12 x x 4 x .

x = 4 7

Got questions? Get instant answers now!

Solve: −3 ( n 2 ) 6 = 21 .

Solution

Remember—always simplify each side first.

.
Distribute. .
Simplify. .
Divide both sides by -3 to isolate n. .
.
Check your answer. Let n = −7 .
.
.
.
.
.
Got questions? Get instant answers now!
Got questions? Get instant answers now!

Solve: −4 ( n 2 ) 8 = 24 .

n = −6

Got questions? Get instant answers now!

Solve: −6 ( n 2 ) 12 = 30 .

n = −5

Got questions? Get instant answers now!

Key concepts

  • Division and Multiplication Properties of Equality
    • Division Property of Equality: For all real numbers a, b, c, and c 0 , if a = b , then a c = b c .
    • Multiplication Property of Equality: For all real numbers a, b, c, if a = b , then a c = b c .

Practice makes perfect

Solve Equations Using the Division and Multiplication Properties of Equality

In the following exercises, solve each equation for the variable using the Division Property of Equality and check the solution.

In the following exercises, solve each equation for the variable using the Multiplication Property of Equality and check the solution.

Solve Equations That Need to be Simplified

In the following exercises, solve the equation.

8 a + 3 a 6 a = −17 + 27

Got questions? Get instant answers now!

6 y 3 y + 12 y = −43 + 28

y = −1

Got questions? Get instant answers now!

−9 x 9 x + 2 x = 50 2

Got questions? Get instant answers now!

−5 m + 7 m 8 m = −6 + 36

m = −5

Got questions? Get instant answers now!

100 16 = 4 p 10 p p

Got questions? Get instant answers now!

−18 7 = 5 t 9 t 6 t

t = 5 2

Got questions? Get instant answers now!

5 12 q + 1 2 q = 25 3

q = 24

Got questions? Get instant answers now!

0.25 d + 0.10 d = 6 0.75

Got questions? Get instant answers now!

0.05 p 0.01 p = 2 + 0.24

p = 56

Got questions? Get instant answers now!

Everyday math

Balloons Ramona bought 18 balloons for a party. She wants to make 3 equal bunches. Find the number of balloons in each bunch, b , by solving the equation 3 b = 18 .

Got questions? Get instant answers now!

Teaching Connie’s kindergarten class has 24 children. She wants them to get into 4 equal groups. Find the number of children in each group, g , by solving the equation 4 g = 24 .

6 children

Got questions? Get instant answers now!

Ticket price Daria paid $36.25 for 5 children’s tickets at the ice skating rink. Find the price of each ticket, p , by solving the equation 5 p = 36.25 .

Got questions? Get instant answers now!

Unit price Nishant paid $12.96 for a pack of 12 juice bottles. Find the price of each bottle, b , by solving the equation 12 b = 12.96 .

$1.08

Got questions? Get instant answers now!

Fuel economy Tania’s SUV gets half as many miles per gallon (mpg) as her husband’s hybrid car. The SUV gets 18 mpg . Find the miles per gallons, m , of the hybrid car, by solving the equation 1 2 m = 18 .

Got questions? Get instant answers now!

Fabric The drill team used 14 yards of fabric to make flags for one-third of the members. Find how much fabric, f , they would need to make flags for the whole team by solving the equation 1 3 f = 14 .

42 yards

Got questions? Get instant answers now!

Writing exercises

Frida started to solve the equation −3 x = 36 by adding 3 to both sides. Explain why Frida’s method will result in the correct solution.

Got questions? Get instant answers now!

Emiliano thinks x = 40 is the solution to the equation 1 2 x = 80 . Explain why he is wrong.

Answer will vary.

Got questions? Get instant answers now!

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 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
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.
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
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
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
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
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

Get the best Algebra and trigonometry course in your pocket!





Source:  OpenStax, Prealgebra. OpenStax CNX. Jul 15, 2016 Download for free at http://legacy.cnx.org/content/col11756/1.9
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

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

Ask