# 8.3 Solve equations with variables and constants on both sides  (Page 5/5)

 Page 5 / 5

## Practice makes perfect

Solve an Equation with Constants on Both Sides

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

$6x-2=40$

$7x-8=34$

6

$11w+6=93$

$14y+7=91$

6

$3a+8=-46$

$4m+9=-23$

−8

$-50=7n-1$

$-47=6b+1$

−8

$25=-9y+7$

$29=-8x-3$

−4

$-12p-3=15$

$-14\text{q}-15=13$

−2

Solve an Equation with Variables on Both Sides

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

$8z=7z-7$

$9k=8k-11$

−11

$4x+36=10x$

$6x+27=9x$

9

$c=-3c-20$

$b=-4b-15$

−3

$5q=44-6q$

$7z=39-6z$

3

$3y+\frac{1}{2}=2y$

$8x+\frac{3}{4}=7x$

−3/4

$-12a-8=-16a$

$-15r-8=-11r$

2

Solve an Equation with Variables and Constants on Both Sides

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

$6x-15=5x+3$

$4x-17=3x+2$

19

$26+8d=9d+11$

$21+6f=7f+14$

7

$3p-1=5p-33$

$8q-5=5q-20$

−5

$4a+5=-a-40$

$9c+7=-2c-37$

−4

$8y-30=-2y+30$

$12x-17=-3x+13$

2

$2\text{z}-4=23-\text{z}$

$3y-4=12-y$

4

$\frac{5}{4}\phantom{\rule{0.1em}{0ex}}c-3=\frac{1}{4}\phantom{\rule{0.1em}{0ex}}c-16$

$\frac{4}{3}\phantom{\rule{0.1em}{0ex}}m-7=\frac{1}{3}\phantom{\rule{0.1em}{0ex}}m-13$

6

$8-\frac{2}{5}\phantom{\rule{0.1em}{0ex}}q=\frac{3}{5}\phantom{\rule{0.1em}{0ex}}q+6$

$11-\frac{1}{4}\phantom{\rule{0.1em}{0ex}}a=\frac{3}{4}\phantom{\rule{0.1em}{0ex}}a+4$

7

$\frac{4}{3}\phantom{\rule{0.1em}{0ex}}n+9=\frac{1}{3}\phantom{\rule{0.1em}{0ex}}n-9$

$\frac{5}{4}\phantom{\rule{0.1em}{0ex}}a+15=\frac{3}{4}\phantom{\rule{0.1em}{0ex}}a-5$

−40

$\frac{1}{4}\phantom{\rule{0.1em}{0ex}}y+7=\frac{3}{4}\phantom{\rule{0.1em}{0ex}}y-3$

$\frac{3}{5}\phantom{\rule{0.1em}{0ex}}p+2=\frac{4}{5}\phantom{\rule{0.1em}{0ex}}p-1$

3

$14n+8.25=9n+19.60$

$13z+6.45=8z+23.75$

3.46

$2.4w-100=0.8w+28$

$2.7w-80=1.2w+10$

60

$5.6r+13.1=3.5r+57.2$

$6.6x-18.9=3.4x+54.7$

23

Solve an Equation Using the General Strategy

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

$5\left(x+3\right)=75$

$4\left(y+7\right)=64$

9

$8=4\left(x-3\right)$

$9=3\left(x-3\right)$

6

$20\left(y-8\right)=-60$

$14\left(y-6\right)=-42$

3

$-4\left(2n+1\right)=16$

$-7\left(3n+4\right)=14$

−2

$3\left(10+5r\right)=0$

$8\left(3+3\text{p}\right)=0$

−1

$\frac{2}{3}\left(9c-3\right)=22$

$\frac{3}{5}\left(10x-5\right)=27$

5

$5\left(1.2u-4.8\right)=-12$

$4\left(2.5v-0.6\right)=7.6$

0.52

$0.2\left(30n+50\right)=28$

$0.5\left(16m+34\right)=-15$

0.25

$-\left(w-6\right)=24$

$-\left(t-8\right)=17$

−9

$9\left(3a+5\right)+9=54$

$8\left(6b-7\right)+23=63$

2

$10+3\left(z+4\right)=19$

$13+2\left(m-4\right)=17$

6

$7+5\left(4-q\right)=12$

$-9+6\left(5-k\right)=12$

3/2

$15-\left(3r+8\right)=28$

$18-\left(9r+7\right)=-16$

3

$11-4\left(y-8\right)=43$

$18-2\left(y-3\right)=32$

−4

$9\left(p-1\right)=6\left(2p-1\right)$

$3\left(4n-1\right)-2=8n+3$

2

$9\left(2m-3\right)-8=4m+7$

$5\left(x-4\right)-4x=14$

34

$8\left(x-4\right)-7x=14$

$5+6\left(3s-5\right)=-3+2\left(8s-1\right)$

10

$-12+8\left(x-5\right)=-4+3\left(5x-2\right)$

$4\left(x-1\right)-8=6\left(3x-2\right)-7$

2

$7\left(2x-5\right)=8\left(4x-1\right)-9$

## 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 $150=2\left(w+15\right)+2w.$

30 feet

Concert tickets At a school concert, the total value of tickets sold was $\text{1,506.}$ Student tickets sold for $\text{6}$ and adult tickets sold for $\text{9.}$ 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 $6s+9\left(3s-5\right)=1506.$

Coins Rhonda has $\text{1.90}$ 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 $0.05n+0.10\left(2n-1\right)=1.90.$

8 nickels

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 $2L+2\left(L-25\right)=74.$

## 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.

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

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

Answers will vary.

Solve the equation $\frac{1}{4}\left(8x+20\right)=3x-4$ explaining all the steps of your solution as in the examples in this section.

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

Answers will vary.

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.

## 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 can chip be made from sand
Eke Reply
is this allso about nanoscale material
Almas
are nano particles real
Missy Reply
yeah
Joseph
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
Lale Reply
no can't
Lohitha
where is the latest information on a no technology how can I find it
William
currently
William
where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
has a lot of application modern world
Kamaluddeen
yes
narayan
what is variations in raman spectra for nanomaterials
Jyoti Reply
ya I also want to know the raman spectra
Bhagvanji
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
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
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
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
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
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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