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Solve an Equation with Constants on Both Sides

In the following exercises, solve the equation for the variable.

−14 q 15 = 13

−2

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Solve an Equation with Variables on Both Sides

In the following exercises, solve the equation for the variable.

−15 r 8 = −11 r

2

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Solve an Equation with Variables and Constants on Both Sides

In the following exercises, solve the equations for the variable.

8 q 5 = 5 q 20

−5

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9 c + 7 = −2 c 37

−4

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8 y 30 = −2 y + 30

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12 x 17 = −3 x + 13

2

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5 4 c 3 = 1 4 c 16

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4 3 m 7 = 1 3 m 13

6

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11 1 4 a = 3 4 a + 4

7

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5 4 a + 15 = 3 4 a 5

−40

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3 5 p + 2 = 4 5 p 1

3

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14 n + 8.25 = 9 n + 19.60

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13 z + 6.45 = 8 z + 23.75

3.46

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2.4 w 100 = 0.8 w + 28

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2.7 w 80 = 1.2 w + 10

60

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5.6 r + 13.1 = 3.5 r + 57.2

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6.6 x 18.9 = 3.4 x + 54.7

23

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Solve an Equation Using the General Strategy

In the following exercises, solve the linear equation using the general strategy.

14 ( y 6 ) = −42

3

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−7 ( 3 n + 4 ) = 14

−2

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3 5 ( 10 x 5 ) = 27

5

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5 ( 1.2 u 4.8 ) = −12

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4 ( 2.5 v 0.6 ) = 7.6

0.52

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0.5 ( 16 m + 34 ) = −15

0.25

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( t 8 ) = 17

−9

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8 ( 6 b 7 ) + 23 = 63

2

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13 + 2 ( m 4 ) = 17

6

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−9 + 6 ( 5 k ) = 12

3/2

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18 ( 9 r + 7 ) = −16

3

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11 4 ( y 8 ) = 43

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18 2 ( y 3 ) = 32

−4

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9 ( p 1 ) = 6 ( 2 p 1 )

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3 ( 4 n 1 ) 2 = 8 n + 3

2

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9 ( 2 m 3 ) 8 = 4 m + 7

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5 ( x 4 ) 4 x = 14

34

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8 ( x 4 ) 7 x = 14

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5 + 6 ( 3 s 5 ) = −3 + 2 ( 8 s 1 )

10

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−12 + 8 ( x 5 ) = −4 + 3 ( 5 x 2 )

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4 ( x 1 ) 8 = 6 ( 3 x 2 ) 7

2

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7 ( 2 x 5 ) = 8 ( 4 x 1 ) 9

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Everyday math

Making a fence Jovani has a fence around the rectangular garden in his backyard. The perimeter of the fence is 150 feet. The length is 15 feet more than the width. Find the width, w , by solving the equation 150 = 2 ( w + 15 ) + 2 w .

30 feet

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Concert tickets At a school concert, the total value of tickets sold was $1,506. Student tickets sold for $6 and adult tickets sold for $9. The number of adult tickets sold was 5 less than 3 times the number of student tickets. Find the number of student tickets sold, s , by solving the equation 6 s + 9 ( 3 s 5 ) = 1506 .

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Coins Rhonda has $1.90 in nickels and dimes. The number of dimes is one less than twice the number of nickels. Find the number of nickels, n , by solving the equation 0.05 n + 0.10 ( 2 n 1 ) = 1.90 .

8 nickels

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Fencing Micah has 74 feet of fencing to make a rectangular dog pen in his yard. He wants the length to be 25 feet more than the width. Find the length, L , by solving the equation 2 L + 2 ( L 25 ) = 74 .

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Writing exercises

When solving an equation with variables on both sides, why is it usually better to choose the side with the larger coefficient as the variable side?

Answers will vary.

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Solve the equation 10 x + 14 = −2 x + 38 , explaining all the steps of your solution.

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What is the first step you take when solving the equation 3 7 ( y 4 ) = 38 ? Explain why this is your first step.

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Solve the equation 1 4 ( 8 x + 20 ) = 3 x 4 explaining all the steps of your solution as in the examples in this section.

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Using your own words, list the steps in the General Strategy for Solving Linear Equations.

Answers will vary.

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Explain why you should simplify both sides of an equation as much as possible before collecting the variable terms to one side and the constant terms to the other side.

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Self check

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

.

What does this checklist tell you about your mastery of this section? What steps will you take to improve?

Questions & Answers

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
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
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
How can I make nanorobot?
Lily
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
how can I make nanorobot?
Lily
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
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

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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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