1. Home
  2. Prealgebra
  3. Integers
  4. Solve equations using integers

3.5 Solve equations using integers; the division property of  (Page 14/5)

<< Chapter < Page
  Prealgebra     Page 1 / 5
Chapter >> Page >
By the end of this section, you will be able to:
  • Determine whether an integer is a solution of an equation
  • Solve equations with integers using the Addition and Subtraction Properties of Equality
  • Model the Division Property of Equality
  • Solve equations using the Division Property of Equality
  • Translate to an equation and solve

Before you get started, take this readiness quiz.

  1. Evaluate x + 4 when x = −4 .
    If you missed this problem, review Evaluate, Simplify and Translate Expressions .
  2. Solve: y − 6 = 10 .
    If you missed this problem, review Solve Equations with the Subtraction and Addition Properties of Equality .
  3. Translate into an algebraic expression 5 less than x .
    If you missed this problem, review Subtract Whole Numbers .

Determine whether a number is a solution of an equation

In Solve Equations with the Subtraction and Addition Properties of Equality , we saw that a solution of an equation is a value of a variable that makes a true statement when substituted into that equation. In that section, we found solutions that were whole numbers. Now that we’ve worked with integers, we’ll find integer solutions to equations.

The steps we take to determine whether a number is a solution to an equation are the same whether the solution is a whole number or an integer.

How to determine whether a number is a solution to an equation.

  1. Substitute the number for the variable in the equation.
  2. Simplify the expressions on both sides of the equation.
  3. Determine whether the resulting equation is true.
    • If it is true, the number is a solution.
    • If it is not true, the number is not a solution.

Determine whether each of the following is a solution of 2 x − 5 = −13 :

  1. ⓐ x = 4
  2. ⓑ x = −4
  3. ⓒ x = −9 .

Solution

ⓐ Substitute 4 for x in the equation to determine if it is true.
.
. .
Multiply. .
Subtract. .

Since x = 4 does not result in a true equation, 4 is not a solution to the equation.

ⓑ Substitute −4 for x in the equation to determine if it is true. .
. .
Multiply. .
Subtract. .

Since x = −4 results in a true equation, −4 is a solution to the equation.

ⓒ Substitute −9 for x in the equation to determine if it is true.
.
Substitute −9 for x. .
Multiply. .
Subtract. .

Since x = −9 does not result in a true equation, −9 is not a solution to the equation.

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

Determine whether each of the following is a solution of 2 x − 8 = −14 :

  1. ⓐ x = −11
  2. ⓑ x = 11
  3. ⓒ x = −3

  1. ⓐ no
  2. ⓑ no
  3. ⓒ yes
Got questions? Get instant answers now!

Determine whether each of the following is a solution of 2 y + 3 = −11 :

  1. ⓐ y = 4
  2. ⓑ y = −4
  3. ⓒ y = −7

  1. ⓐ no
  2. ⓑ no
  3. ⓒ yes
Got questions? Get instant answers now!

Solve equations with integers using the addition and subtraction properties of equality

In Solve Equations with the Subtraction and Addition Properties of Equality , we solved equations similar to the two shown here using the Subtraction and Addition Properties of Equality. Now we can use them again with integers.

This figure has two columns. The first column has the equation x plus 4 equals 12. Underneath there is x plus 4 minus 4 equals 12 minus 4. Under this there is x equals 8. The second column has the equation y minus 5 equals 9. Underneath there is the equation y minus 5 plus 5 equals 9 plus 5. Under this there is y equals 14.

When you add or subtract the same quantity from both sides of an equation, you still have equality.

Properties of equalities

Subtraction Property of Equality Addition Property of Equality
For any numbers a , b , c ,
if a = b then a − c = b − c . 		For any numbers a , b , c ,
if a = b then a + c = b + c .

Solve: y + 9 = 5 .

Solution

.
Subtract 9 from each side to undo the addition. .
Simplify. .

Check the result by substituting −4 into the original equation.

y + 9 = 5
Substitute −4 for y −4 + 9 = ? 5
5 = 5 ✓

Since y = −4 makes y + 9 = 5 a true statement, we found the solution to this equation.

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

Questions & Answers

the definition for anatomy and physiology
Watta Reply
what is microbiology
Agebe Reply
What is a cell
Odelana Reply
what is cell
Mohammed
how does Neisseria cause meningitis
Nyibol Reply
what is microbiologist
Muhammad Reply
what is errata
Muhammad
is the branch of biology that deals with the study of microorganisms.
Ntefuni Reply
What is microbiology
Mercy Reply
studies of microbes
Louisiaste
when we takee the specimen which lumbar,spin,
Ziyad Reply
How bacteria create energy to survive?
Muhamad Reply
Bacteria doesn't produce energy they are dependent upon their substrate in case of lack of nutrients they are able to make spores which helps them to sustain in harsh environments
_Adnan
But not all bacteria make spores, l mean Eukaryotic cells have Mitochondria which acts as powerhouse for them, since bacteria don't have it, what is the substitution for it?
Muhamad
they make spores
Louisiaste
what is sporadic nd endemic, epidemic
Aminu Reply
the significance of food webs for disease transmission
Abreham
food webs brings about an infection as an individual depends on number of diseased foods or carriers dully.
Mark
explain assimilatory nitrate reduction
Esinniobiwa Reply
Assimilatory nitrate reduction is a process that occurs in some microorganisms, such as bacteria and archaea, in which nitrate (NO3-) is reduced to nitrite (NO2-), and then further reduced to ammonia (NH3).
Elkana
This process is called assimilatory nitrate reduction because the nitrogen that is produced is incorporated in the cells of microorganisms where it can be used in the synthesis of amino acids and other nitrogen products
Elkana
Examples of thermophilic organisms
Shu Reply
Give Examples of thermophilic organisms
Shu
advantages of normal Flora to the host
Micheal Reply
Prevent foreign microbes to the host
Abubakar
they provide healthier benefits to their hosts
ayesha
They are friends to host only when Host immune system is strong and become enemies when the host immune system is weakened . very bad relationship!
Mark
what is cell
faisal Reply
cell is the smallest unit of life
Fauziya
cell is the smallest unit of life
Akanni
ok
Innocent
cell is the structural and functional unit of life
Hasan
is the fundamental units of Life
Musa
what are emergency diseases
Micheal Reply
There are nothing like emergency disease but there are some common medical emergency which can occur simultaneously like Bleeding,heart attack,Breathing difficulties,severe pain heart stock.Hope you will get my point .Have a nice day ❣️
_Adnan
define infection ,prevention and control
Innocent
I think infection prevention and control is the avoidance of all things we do that gives out break of infections and promotion of health practices that promote life
Lubega
Heyy Lubega hussein where are u from?
_Adnan
en français
Adama
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply
<< Chapter < Page Page > Chapter >>

Read also:

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




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