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Think about twin brothers Andy and Bobby. They are 17 years old. How old was Andy 3 years ago? He was 3 years less than 17 , so his age was 17 3 , or 14 . What about Bobby’s age 3 years ago? Of course, he was 14 also. Their ages are equal now, and subtracting the same quantity from both of them resulted in equal ages 3 years ago.

a = b a 3 = b 3

Solve an equation using the subtraction property of equality.

  1. Use the Subtraction Property of Equality to isolate the variable.
  2. Simplify the expressions on both sides of the equation.
  3. Check the solution.

Solve: x + 8 = 17 .

Solution

We will use the Subtraction Property of Equality to isolate x .

.
Subtract 8 from both sides. .
Simplify. .
.
.
.

Since x = 9 makes x + 8 = 17 a true statement, we know 9 is the solution to the equation.

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Solve:

x + 6 = 19

x = 13

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Solve: 100 = y + 74 .

Solution

To solve an equation, we must always isolate the variable—it doesn’t matter which side it is on. To isolate y , we will subtract 74 from both sides.

.
Subtract 74 from both sides. .
Simplify. .
Substitute 26 for y to check.
The image shows the original equation,100 equal to y plus 74. Substitute 26 in for y to check. The equation becomes 100 equal to 26 plus 74. Is this true? The right side simplifies by adding 26 and 74 to get 100. Both sides of the equal symbol are 100.

Since y = 26 makes 100 = y + 74 a true statement, we have found the solution to this equation.

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Solve:

95 = y + 67

y = 28

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Solve:

91 = y + 45

y = 46

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Solve equations using the addition property of equality

In all the equations we have solved so far, a number was added to the variable on one side of the equation. We used subtraction to “undo” the addition in order to isolate the variable.

But suppose we have an equation with a number subtracted from the variable, such as x 5 = 8 . We want to isolate the variable, so to “undo” the subtraction we will add the number to both sides.

We use the Addition Property of Equality, which says we can add the same number to both sides of the equation without changing the equality. Notice how it mirrors the Subtraction Property of Equality.

Addition property of equality

For any numbers a , b , and c , if

a = b

then

a + c = b + c

Remember the 17 -year-old twins, Andy and Bobby? In ten years, Andy’s age will still equal Bobby’s age. They will both be 27 .

a = b a + 10 = b + 10

We can add the same number to both sides and still keep the equality.

Solve an equation using the addition property of equality.

  1. Use the Addition Property of Equality to isolate the variable.
  2. Simplify the expressions on both sides of the equation.
  3. Check the solution.

Solve: x 5 = 8 .

Solution

We will use the Addition Property of Equality to isolate the variable.

.
Add 5 to both sides. .
Simplify. .
.
.
.
.

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Solve:

x 9 = 13

x = 22

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Solve:

y 1 = 3

y = 4

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Solve: 27 = a 16 .

Solution

We will add 16 to each side to isolate the variable.

.
Add 16 to each side. .
Simplify. .
. .
.
.

The solution to 27 = a 16 is a = 43 .

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Solve:

19 = a 18

a = 37

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Solve:

27 = n 14

n = 41

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Translate word phrases to algebraic equations

Remember, an equation has an equal sign between two algebraic expressions. So if we have a sentence that tells us that two phrases are equal, we can translate it into an equation. We look for clue words that mean equals . Some words that translate to the equal sign are:

  • is equal to
  • is the same as
  • is
  • gives
  • was
  • will be

It may be helpful to put a box around the equals word(s) in the sentence to help you focus separately on each phrase. Then translate each phrase into an expression, and write them on each side of the equal sign.

Questions & Answers

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s. Reply
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Devang Reply
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s.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
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what's the easiest and fastest way to the synthesize AgNP?
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Cied
types of nano material
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I start with an easy one. carbon nanotubes woven into a long filament like a string
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Porter
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what is the function of carbon nanotubes?
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I'm interested in nanotube
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what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
AMJAD
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AMJAD
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
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after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
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name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
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silver nanoparticles could handle the job?
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not now but maybe in future only AgNP maybe any other nanomaterials
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Hello
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I'm interested in Nanotube
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this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
can nanotechnology change the direction of the face of the world
Prasenjit Reply
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Practice Key Terms 1

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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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