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SubtractSides
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SubtractSides

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SubtractSides[rel,x]

subtracts x from each side of the equation or inequality rel.

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SubtractSides[rel1,rel2]

subtracts the corresponding sides of two equations or inequalities.

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subtracts the right-hand side of rel from each side, producing a zero right-hand side.

Details

  • The relations rel can have any of the following forms:
  • lhs==rhsequations
    lhs!=rhsinequations
    lhs>rhs or lhs>=rhs inequalities
    ab>c≥…generalized inequalities

Examples

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Basic Examples  (4)Summary of the most common use cases

Subtract 3 from both sides of an equation:

In[1]:=1
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https://wolfram.com/xid/0b0jzbmhjq0-8w52hw
Out[1]=1

Subtract the right-hand side of an equation from both sides:

In[1]:=1
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https://wolfram.com/xid/0b0jzbmhjq0-5ynxpa
Out[1]=1

Subtract the corresponding sides of two equations:

In[1]:=1
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https://wolfram.com/xid/0b0jzbmhjq0-g2iotm
Out[1]=1

Subtract the number b from both sides of an inequality:

In[1]:=1
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https://wolfram.com/xid/0b0jzbmhjq0-eh0yny
Out[1]=1

Scope  (6)Survey of the scope of standard use cases

Subtract the rightmost side from each side of an equation with three expressions:

In[2]:=2
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https://wolfram.com/xid/0b0jzbmhjq0-49hnn5
Out[2]=2

Combine an equation and an inequation:

In[1]:=1
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https://wolfram.com/xid/0b0jzbmhjq0-5gunuo
Out[1]=1

Combine an equation and an inequality:

In[1]:=1
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https://wolfram.com/xid/0b0jzbmhjq0-86va4h
Out[1]=1

Subtract from each part of a generalized inequality:

In[1]:=1
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https://wolfram.com/xid/0b0jzbmhjq0-f61i3v
Out[1]=1

Subtract x^2 from several inequalities expressed using Piecewise:

In[1]:=1
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https://wolfram.com/xid/0b0jzbmhjq0-eghb40
Out[1]=1

Subtract the right-hand side from both sides of an equation inside ConditionalExpression:

In[1]:=1
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https://wolfram.com/xid/0b0jzbmhjq0-eyvuq1
Out[1]=1

Applications  (1)Sample problems that can be solved with this function

Derive the quadratic formula:

In[1]:=1
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https://wolfram.com/xid/0b0jzbmhjq0-ya5z48
Out[1]=1

Multiply both sides by 4 a:

In[2]:=2
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https://wolfram.com/xid/0b0jzbmhjq0-p4zxbs
Out[2]=2

Subtract 4 a c-b^2 from both sides:

In[3]:=3
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https://wolfram.com/xid/0b0jzbmhjq0-lxuas
Out[3]=3

Factor the left-hand side:

In[4]:=4
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https://wolfram.com/xid/0b0jzbmhjq0-z9vobs
Out[4]=4

Take the positive square root of both sides:

In[5]:=5
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https://wolfram.com/xid/0b0jzbmhjq0-jgoyi6
Out[5]=5

Cancel the square root of the square:

In[6]:=6
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https://wolfram.com/xid/0b0jzbmhjq0-jow5s0
Out[6]=6

Subtract b from both sides:

In[7]:=7
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https://wolfram.com/xid/0b0jzbmhjq0-gg72b8
Out[7]=7

Divide both sides by 2 a to obtain the quadratic formula for x with positive square root:

In[8]:=8
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https://wolfram.com/xid/0b0jzbmhjq0-nsnzl9
Out[8]=8

Properties & Relations  (4)Properties of the function, and connections to other functions

True and False are considered trivial equations:

In[1]:=1
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https://wolfram.com/xid/0b0jzbmhjq0-cvp7r6
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0b0jzbmhjq0-j1uqt0
Out[2]=2

SubtractSides transforms equations to equivalent equations:

In[1]:=1
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https://wolfram.com/xid/0b0jzbmhjq0-mn7i8b
Out[1]=1

Solve gives values for the variables that make the equation true:

In[2]:=2
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https://wolfram.com/xid/0b0jzbmhjq0-wii2e9
Out[2]=2

Reduce can be used to rewrite an equation in the form var==value:

In[3]:=3
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https://wolfram.com/xid/0b0jzbmhjq0-stylix
Out[3]=3

Simplify includes the functionality of SubtractSides:

In[1]:=1
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https://wolfram.com/xid/0b0jzbmhjq0-iol8qk
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0b0jzbmhjq0-9c30qu
Out[2]=2

SubtractSides[eq,x] is the inverse of AddSides[eq,x]:

In[1]:=1
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https://wolfram.com/xid/0b0jzbmhjq0-l9zzrm
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0b0jzbmhjq0-qaa93s
Out[2]=2
Wolfram Research (2018), SubtractSides, Wolfram Language function, https://reference.wolfram.com/language/ref/SubtractSides.html.
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Wolfram Research (2018), SubtractSides, Wolfram Language function, https://reference.wolfram.com/language/ref/SubtractSides.html.

Text

Wolfram Research (2018), SubtractSides, Wolfram Language function, https://reference.wolfram.com/language/ref/SubtractSides.html.

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Wolfram Research (2018), SubtractSides, Wolfram Language function, https://reference.wolfram.com/language/ref/SubtractSides.html.

CMS

Wolfram Language. 2018. "SubtractSides." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/SubtractSides.html.

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Wolfram Language. 2018. "SubtractSides." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/SubtractSides.html.

APA

Wolfram Language. (2018). SubtractSides. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SubtractSides.html

✖
Wolfram Language. (2018). SubtractSides. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SubtractSides.html

BibTeX

@misc{reference.wolfram_2025_subtractsides, author="Wolfram Research", title="{SubtractSides}", year="2018", howpublished="\url{https://reference.wolfram.com/language/ref/SubtractSides.html}", note=[Accessed: 26-April-2025 ]}

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@misc{reference.wolfram_2025_subtractsides, author="Wolfram Research", title="{SubtractSides}", year="2018", howpublished="\url{https://reference.wolfram.com/language/ref/SubtractSides.html}", note=[Accessed: 26-April-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_subtractsides, organization={Wolfram Research}, title={SubtractSides}, year={2018}, url={https://reference.wolfram.com/language/ref/SubtractSides.html}, note=[Accessed: 26-April-2025 ]}

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@online{reference.wolfram_2025_subtractsides, organization={Wolfram Research}, title={SubtractSides}, year={2018}, url={https://reference.wolfram.com/language/ref/SubtractSides.html}, note=[Accessed: 26-April-2025 ]}