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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

find the 15th term of the geometric sequince whose first is 18 and last term of 387
Jerwin Reply
The given of f(x=x-2. then what is the value of this f(3) 5f(x+1)
virgelyn Reply
hmm well what is the answer
Abhi
how do they get the third part x = (32)5/4
kinnecy Reply
can someone help me with some logarithmic and exponential equations.
Jeffrey Reply
sure. what is your question?
ninjadapaul
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
ninjadapaul
I don't understand what the A with approx sign and the boxed x mean
ninjadapaul
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
ninjadapaul
oops. ignore that.
ninjadapaul
so you not have an equal sign anywhere in the original equation?
ninjadapaul
hmm
Abhi
is it a question of log
Abhi
🤔.
Abhi
Commplementary angles
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right! what he said ⤴⤴⤴
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what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
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algebra 2 Inequalities:If equation 2 = 0 it is an open set?
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or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
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Kristine 2*2*2=8
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Differences Between Laspeyres and Paasche Indices
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No. 7x -4y is simplified from 4x + (3y + 3x) -7y
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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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Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
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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
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anybody can imagine what will be happen after 100 years from now in nano tech world
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Prasenjit
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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
Azam
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
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Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
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the Beer law works very well for dilute solutions but fails for very high concentrations. why?
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how do you translate this in Algebraic Expressions
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Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
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. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
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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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