<< Chapter < Page Chapter >> Page >

Solve 3 ( m 6 ) 2 m = 4 + 1 for m .

3 ( m 6 ) 2 m = 4 + 1 3 m 18 2 m = 3 m 18 = 3 m = 15

C h e c k : 3 ( 15 6 ) 2 ( 15 ) = 4 + 1 Is this correct? 3 ( 9 ) 30 = 3 Is this correct? 27 30 = 3 Is this correct? 3 = 3 Yes, this is correct .

Got questions? Get instant answers now!

Practice set b

Solve and check each equation.

16 x 3 15 x = 8 for x .

x = 11

Got questions? Get instant answers now!

4 ( y 5 ) 3 y = 1 for y .

y = 19

Got questions? Get instant answers now!

2 ( a 2 + 3 a 1 ) + 2 a 2 + 7 a = 0 for a .

a = 2

Got questions? Get instant answers now!

5 m ( m 2 a 1 ) 5 m 2 + 2 a ( 5 m + 3 ) = 10 for a .

a = 10 + 5 m 6

Got questions? Get instant answers now!

Often the variable we wish to solve for will appear on both sides of the equal sign. We can isolate the variable on either the left or right side of the equation by using the techniques of Sections [link] and [link] .

Sample set c

Solve 6 x 4 = 2 x + 8 for x .

6 x 4 = 2 x + 8 To isolate x on the left side, subtract 2 m from both sides . 6 x 4 2 x = 2 x + 8 2 x 4 x 4 = 8 Add 4 to both sides . 4 x 4 + 4 = 8 + 4 4 x = 12 Divide both sides by 4. 4 x 4 = 12 4 x = 3

C h e c k : 6 ( 3 ) 4 = 2 ( 3 ) + 8 Is this correct? 18 4 = 6 + 8 Is this correct? 14 = 14 Yes, this is correct .

Got questions? Get instant answers now!

Solve 6 ( 1 3 x ) + 1 = 2 x [ 3 ( x 7 ) 20 ] for x .

On left side of an equation, arrows show that six is multiplied with each term inside the parentheses, and on right side, arrows show that three is multiplied with each term inside the parentheses.

6 18 x + 1 = 2 x [ 3 x 21 20 ] 18 x + 7 = 2 x [ 3 x 41 ] 18 x + 7 = 2 x 3 x + 41 18 x + 7 = x + 41 To isolate x on the right side, add 18 x to both sides . 18 x + 7 + 18 x = x + 41 + 18 x 7 = 17 x + 41 Subtract 41 from both sides . 7 41 = 17 x + 41 41 34 = 17 x Divide both sides by 17. 34 17 = 17 x 17 2 = x Since the equation 2 = x is equivalent to the equation x = 2 , we can write the answer as x = 2. x = 2

C h e c k : 6 ( 1 3 ( 2 ) ) + 1 = 2 ( 2 ) [ 3 ( 2 7 ) 20 ] Is this correct? 6 ( 1 + 6 ) + 1 = 4 [ 3 ( 9 ) 20 ] Is this correct? 6 ( 7 ) + 1 = 4 [ 27 20 ] Is this correct? 42 + 1 = 4 [ 47 ] Is this correct? 43 = 4 + 47 Is this correct? 43 = 43 Yes, this is correct .

Got questions? Get instant answers now!

Practice set c

Solve 8 a + 5 = 3 a 5 for a .

a = 2

Got questions? Get instant answers now!

Solve 9 y + 3 ( y + 6 ) = 15 y + 21 for y .

y = 1

Got questions? Get instant answers now!

Solve 3 k + 2 [ 4 ( k 1 ) + 3 ] = 63 2 k for k .

k = 5

Got questions? Get instant answers now!

Recognizing identities and contradictions

As we noted in Section [link] , some equations are identities and some are contradictions. As the problems of Sample Set D will suggest,

    Recognizing an identity

  1. If, when solving an equation, all the variables are eliminated and a true statement results, the equation is an identity.

    Recognizing a contradiction

  1. If, when solving an equation, all the variables are eliminated and a false statement results, the equation is a contradiction.

Sample set d

Solve 9 x + 3 ( 4 3 x ) = 12 for x .

On left side of an equation, arrows show that three is multiplied with each term inside the parentheses.

9 x + 12 9 x = 12 12 = 12

The variable has been eliminated and the result is a true statement. The original equation is an identity.

Got questions? Get instant answers now!

Solve 2 ( 10 2 y ) 4 y + 1 = 18 for y .

On left side of an equation, arrows show that negative two is multiplied with each term inside the parentheses.

20 + 4 y 4 y + 1 = 18 19 = 18

The variable has been eliminated and the result is a false statement. The original equation is a contradiction.

Got questions? Get instant answers now!

Practice set d

Classify each equation as an identity or a contradiction.

6 x + 3 ( 1 2 x ) = 3

identity, 3 = 3

Got questions? Get instant answers now!

8 m + 4 ( 2 m 7 ) = 28

contradiction, 28 = 28

Got questions? Get instant answers now!

3 ( 2 x 4 ) 2 ( 3 x + 1 ) + 14 = 0

identity, 0 = 0

Got questions? Get instant answers now!

5 ( x + 6 ) + 8 = 3 [ 4 ( x + 2 ) ] 2 x

contradiction, 22 = 6

Got questions? Get instant answers now!

Exercises

For the following problems, solve each conditional equation. If the equation is not conditional, identify it as an identity or a contradiction.

2 y + 7 = 3

y = 5

Got questions? Get instant answers now!

5 x + 6 = 9

x = 3

Got questions? Get instant answers now!

10 y 3 = 23

y = 2

Got questions? Get instant answers now!

m 11 15 = 19

m = 44

Got questions? Get instant answers now!

7 x 4 + 6 = 8

x = 8

Got questions? Get instant answers now!

3 k 14 + 25 = 22

k = 14

Got questions? Get instant answers now!

3 ( x 6 ) + 5 = 25

Got questions? Get instant answers now!

16 ( y 1 ) + 11 = 85

y = 5

Got questions? Get instant answers now!

23 y 19 = 22 y + 1

y = 20

Got questions? Get instant answers now!

8 k + 7 = 2 k + 1

k = 1

Got questions? Get instant answers now!

2 ( x 7 ) = 2 x + 5

contradiction

Got questions? Get instant answers now!

4 ( 5 y + 3 ) + 5 ( 1 + 4 y ) = 0

Got questions? Get instant answers now!

3 x + 7 = 3 ( x + 2 )

x = 3

Got questions? Get instant answers now!

4 ( 4 y + 2 ) = 3 y + 2 [ 1 3 ( 1 2 y ) ]

Got questions? Get instant answers now!

5 ( 3 x 8 ) + 11 = 2 2 x + 3 ( x 4 )

x = 19 14

Got questions? Get instant answers now!

12 ( m 2 ) = 2 m + 3 m 2 m + 3 ( 5 3 m )

Got questions? Get instant answers now!

4 k ( 4 3 k ) = 3 k 2 k ( 3 6 k ) + 1

k = 3

Got questions? Get instant answers now!

3 [ 4 2 ( y + 2 ) ] = 2 y 4 [ 1 + 2 ( 1 + y ) ]

Got questions? Get instant answers now!

5 [ 2 m ( 3 m 1 ) ] = 4 m 3 m + 2 ( 5 2 m ) + 1

m = 2

Got questions? Get instant answers now!

For the following problems, solve the literal equations for the indicated variable. When directed, find the value of that variable for the given values of the other variables.

Solve I = E R for R . Find the value of R when I = 0.005 and E = 0.0035.

Got questions? Get instant answers now!

Solve P = R C for R . Find the value of R when P = 27 and C = 85.

R = 112

Got questions? Get instant answers now!

Solve z = x x ¯ s for x . Find the value of x when z = 1.96 , s = 2.5 , and x ¯ = 15.

Got questions? Get instant answers now!

Solve F = S x 2 S y 2 for S x 2 S x 2 represents a single quantity. Find the value of S x 2 when F = 2.21 and S y 2 = 3.24.

S x 2 = F · S y 2 ; S x 2 = 7.1604

Got questions? Get instant answers now!

Solve p = n R T V for R .

Got questions? Get instant answers now!

Solve x = 4 y + 7 for y .

y = x 7 4

Got questions? Get instant answers now!

Solve y = 10 x + 16 for x .

Got questions? Get instant answers now!

Solve 2 x + 5 y = 12 for y .

y = 2 x + 12 5

Got questions? Get instant answers now!

Solve 9 x + 3 y + 15 = 0 for y .

Got questions? Get instant answers now!

Solve m = 2 n h 5 for n .

n = 5 m + h 2

Got questions? Get instant answers now!

Solve t = Q + 6 P 8 for P .

Got questions? Get instant answers now!

Solve A star = + 9 j Δ for j .

j is equal to the product of star and triangle minus square over nine.

Got questions? Get instant answers now!

Exercises for review

( [link] ) Simplify ( x + 3 ) 2 ( x 2 ) 3 ( x 2 ) 4 ( x + 3 ) .

( x + 3 ) 3 ( x 2 ) 7

Got questions? Get instant answers now!

( [link] ) Find the product. ( x 7 ) ( x + 7 ) .

Got questions? Get instant answers now!

( [link] ) Find the product. ( 2 x 1 ) 2 .

4 x 2 4 x + 1

Got questions? Get instant answers now!

( [link] ) Solve the equation y 2 = 2.

Got questions? Get instant answers now!

( [link] ) Solve the equation 4 x 5 = 3.

x = 15 4

Got questions? Get instant answers now!

Questions & Answers

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
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
can nanotechnology change the direction of the face of the world
Prasenjit 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
Please keep in mind that it's not allowed to promote any social groups (whatsapp, facebook, etc...), exchange phone numbers, email addresses or ask for personal information on QuizOver's platform.
QuizOver Reply

Get the best Algebra and trigonometry course in your pocket!





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