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

3.5 Solve equations using integers; the division property of

<< 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

I'm interested in biological psychology and cognitive psychology
Tanya Reply
what does preconceived mean
sammie Reply
physiological Psychology
Nwosu Reply
How can I develope my cognitive domain
Amanyire Reply
why is communication effective
Dakolo Reply
Communication is effective because it allows individuals to share ideas, thoughts, and information with others.
effective communication can lead to improved outcomes in various settings, including personal relationships, business environments, and educational settings. By communicating effectively, individuals can negotiate effectively, solve problems collaboratively, and work towards common goals.
it starts up serve and return practice/assessments.it helps find voice talking therapy also assessments through relaxed conversation.
miss
Every time someone flushes a toilet in the apartment building, the person begins to jumb back automatically after hearing the flush, before the water temperature changes. Identify the types of learning, if it is classical conditioning identify the NS, UCS, CS and CR. If it is operant conditioning, identify the type of consequence positive reinforcement, negative reinforcement or punishment
Wekolamo Reply
please i need answer
Wekolamo
because it helps many people around the world to understand how to interact with other people and understand them well, for example at work (job).
Manix Reply
Agreed 👍 There are many parts of our brains and behaviors, we really need to get to know. Blessings for everyone and happy Sunday!
ARC
A child is a member of community not society elucidate ?
JESSY Reply
Isn't practices worldwide, be it psychology, be it science. isn't much just a false belief of control over something the mind cannot truly comprehend?
Simon Reply
compare and contrast skinner's perspective on personality development on freud
namakula Reply
Skinner skipped the whole unconscious phenomenon and rather emphasized on classical conditioning
war
explain how nature and nurture affect the development and later the productivity of an individual.
Amesalu Reply
nature is an hereditary factor while nurture is an environmental factor which constitute an individual personality. so if an individual's parent has a deviant behavior and was also brought up in an deviant environment, observation of the behavior and the inborn trait we make the individual deviant.
Samuel
I am taking this course because I am hoping that I could somehow learn more about my chosen field of interest and due to the fact that being a PsyD really ignites my passion as an individual the more I hope to learn about developing and literally explore the complexity of my critical thinking skills
Zyryn Reply
good👍
Jonathan
and having a good philosophy of the world is like a sandwich and a peanut butter 👍
Jonathan
generally amnesi how long yrs memory loss
Kelu Reply
interpersonal relationships
Abdulfatai Reply
What would be the best educational aid(s) for gifted kids/savants?
Heidi Reply
treat them normal, if they want help then give them. that will make everyone happy
Saurabh
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