<< Chapter < Page Chapter >> Page >

Solve: a 3.93 = −2.86 .

a = 1.07

Got questions? Get instant answers now!

Solve: n 3.47 = −2.64 .

n = 0.83

Got questions? Get instant answers now!

Solve: −4.8 = 0.8 n .

Solution

We will use the Division Property of Equality.

Use the Properties of Equality to find a value for n .

.
We must divide both sides by 0.8 to isolate n . .
Simplify. .
Check: .
. .
.

Since n = −6 makes −4.8 = 0.8 n a true statement, we know we have a solution.

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

Solve: −8.4 = 0.7 b .

b = −12

Got questions? Get instant answers now!

Solve: −5.6 = 0.7 c .

c = −8

Got questions? Get instant answers now!

Solve: p 1.8 = −6.5 .

Solution

We will use the Multiplication Property of Equality .

.
Here, p is divided by −1.8. We must multiply by −1.8 to isolate p .
Multiply. .
Check: .
. .
.

A solution to p −1.8 = −6.5 is p = 11.7 .

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

Solve: c −2.6 = −4.5 .

c = 11.7

Got questions? Get instant answers now!

Solve: b −1.2 = −5.4 .

b = 6.48

Got questions? Get instant answers now!

Translate to an equation and solve

Now that we have solved equations with decimals, we are ready to translate word sentences to equations and solve. Remember to look for words and phrases that indicate the operations to use.

Translate and solve: The difference of n and 4.3 is 2.1 .

Solution

Translate. .
Add 4.3 to both sides of the equation. .
Simplify. .
Check: Is the difference of n and 4.3 equal to 2.1? .
Let n = 4.3 : Is the difference of 6.4 and 4.3 equal to 2.1?
Translate. .
Simplify. .
Got questions? Get instant answers now!
Got questions? Get instant answers now!

Translate and solve: The difference of y and 4.9 is 2.8 .

y − 4.9 = 2.8; y = 7.7

Got questions? Get instant answers now!

Translate and solve: The difference of z and 5.7 is 3.4 .

z − 5.7 = 3.4; z = 9.1

Got questions? Get instant answers now!

Translate and solve: The product of −3.1 and x is 5.27 .

Solution

Translate. .
Divide both sides by −3.1 . .
Simplify. .
Check: Is the product of −3.1 and x equal to 5.27 ? .
Let x = −1.7 : Is the product of −3.1 and −1.7 equal to 5.27 ?
Translate. .
Simplify. .
Got questions? Get instant answers now!
Got questions? Get instant answers now!

Translate and solve: The product of −4.3 and x is 12.04 .

−4.3 x = 12.04; x = −2.8

Got questions? Get instant answers now!

Translate and solve: The product of −3.1 and m is 26.66 .

−3.1 m = 26.66; m = −8.6

Got questions? Get instant answers now!

Translate and solve: The quotient of p and −2.4 is 6.5 .

Solution

Translate. .
Multiply both sides by −2.4 . .
Simplify. .
Check: Is the quotient of p and −2.4 equal to 6.5 ? .
Let p = −15.6 : Is the quotient of −15.6 and −2.4 equal to 6.5 ?
Translate. .
Simplify. .
Got questions? Get instant answers now!
Got questions? Get instant answers now!

Translate and solve: The quotient of q and −3.4 is 4.5 .

q −3.4 = 4.5 ; q = −15.3

Got questions? Get instant answers now!

Translate and solve: The quotient of r and −2.6 is 2.5 .

r −2.6 = 2.5 ; r = −6.5

Got questions? Get instant answers now!

Translate and solve: The sum of n and 2.9 is 1.7 .

Solution

Translate. .
Subtract 2.9 from each side. .
Simplify. .
Check: Is the sum n and 2.9 equal to 1.7 ? .
Let n = −1.2 : Is the sum −1.2 and 2.9 equal to 1.7 ?
Translate. .
Simplify. .
Got questions? Get instant answers now!
Got questions? Get instant answers now!

Translate and solve: The sum of j and 3.8 is 2.6 .

j + 3.8 = 2.6; j = −1.2

Got questions? Get instant answers now!

Translate and solve: The sum of k and 4.7 is 0.3 .

k + 4.7 = 0.3; k = −4.4

Got questions? Get instant answers now!

Key concepts

  • Determine whether a number is a solution to an equation.
    • Substitute the number for the variable in the equation.
    • Simplify the expressions on both sides of the equation.
    • Determine whether the resulting equation is true.
      If so, the number is a solution.
      If not, the number is not a solution.
  • Properties of Equality
Subtraction Property of Equality Addition Property of Equality
For any numbers a , b , and c ,
If a = b then a c = b c
For any numbers a , b , and c ,
If a = b then a + c = b + c
Division of Property of Equality Multiplication Property of Equality
For any numbers a , b , and c 0 ,
If a = b then a c = b c
For any numbers a , b , and c ,
If a = b then a c = b c

Practice makes perfect

Determine Whether a Decimal is a Solution of an Equation

In the following exercises, determine whether each number is a solution of the given equation.

x 0.8 = 2.3
x = 2 x = −1.5 x = 3.1

  1. no
  2. no
  3. yes

Got questions? Get instant answers now!

y + 0.6 = −3.4
y = −4 y = −2.8 y = 2.6

Got questions? Get instant answers now!

h 1.5 = −4.3
h = 6.45 h = −6.45 h = −2.1

  1. no
  2. yes
  3. no

Got questions? Get instant answers now!

0.75 k = −3.6
k = −0.48 k = −4.8 k = −2.7

Got questions? Get instant answers now!

Solve Equations with Decimals

In the following exercises, solve the equation.

f + 3.45 = 2.6

f = −0.85

Got questions? Get instant answers now!

a + 6.2 = −1.7

a = −7.9

Got questions? Get instant answers now!

c + 1.15 = −3.5

c = −4.65

Got questions? Get instant answers now!

x 0.4 = −3.9

x = −3.5

Got questions? Get instant answers now!

j 1.82 = −6.5

j = −4.68

Got questions? Get instant answers now!

m 0.25 = −1.67

m = −1.42

Got questions? Get instant answers now!

−120 = 1.5 q

q = −80

Got questions? Get instant answers now!

−3.4 z = −9.18

z = 2.7

Got questions? Get instant answers now!

x 0.7 = −0.4

x = −0.28

Got questions? Get instant answers now!

p 5 = −1.65

p = 8.25

Got questions? Get instant answers now!

r 1.2 = −6

r = 7.2

Got questions? Get instant answers now!

Mixed Practice

In the following exercises, solve the equation. Then check your solution.

x 5 = −11

x = −6

Got questions? Get instant answers now!

−4.2 m = −33.6

m = 8

Got questions? Get instant answers now!

q + 5 6 = 1 12

q = 3 4

Got questions? Get instant answers now!

2 3 = y + 3 8

y = 25 24

Got questions? Get instant answers now!

11 20 = f

f = 11 20

Got questions? Get instant answers now!

−4.2 a = 3.36

a = −0.8

Got questions? Get instant answers now!

r 1.25 = −2.7

r = −1.45

Got questions? Get instant answers now!

Translate to an Equation and Solve

In the following exercises, translate and solve.

The difference of n and 1.9 is 3.4 .

n 1.9 = 3.4 ; 5.3

Got questions? Get instant answers now!

The difference n and 1.5 is 0.8 .

Got questions? Get instant answers now!

The product of −6.2 and x is −4.96 .

−6.2 x = −4.96; 0.8

Got questions? Get instant answers now!

The product of −4.6 and x is −3.22 .

Got questions? Get instant answers now!

The quotient of y and −1.7 is −5 .

y 1.7 = −5 ; 8.5

Got questions? Get instant answers now!

The quotient of z and −3.6 is 3 .

Got questions? Get instant answers now!

The sum of n and −7.3 is 2.4.

n + (−7.3) = 2.4; 9.7

Got questions? Get instant answers now!

The sum of n and −5.1 is 3.8 .

Got questions? Get instant answers now!

Everyday math

Shawn bought a pair of shoes on sale for $78 . Solve the equation 0.75 p = 78 to find the original price of the shoes, p .

$104

Got questions? Get instant answers now!

Mary bought a new refrigerator. The total price including sales tax was $1,350 . Find the retail price, r , of the refrigerator before tax by solving the equation 1.08 r = 1,350 .

Got questions? Get instant answers now!

Writing exercises

Think about solving the equation 1.2 y = 60 , but do not actually solve it. Do you think the solution should be greater than 60 or less than 60 ? Explain your reasoning. Then solve the equation to see if your thinking was correct.

Answers will vary.

Got questions? Get instant answers now!

Think about solving the equation 0.8 x = 200 , but do not actually solve it. Do you think the solution should be greater than 200 or less than 200 ? Explain your reasoning. Then solve the equation to see if your thinking was correct.

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.

.

On a scale of 1–10, how would you rate your mastery of this section in light of your responses on the checklist? How can you improve this?

Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
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
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
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
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
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
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
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

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