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AddSides[rel,x]

adds x to each side of the equation or inequality rel.

AddSides[rel1,rel2]

adds the corresponding sides of two equations or inequalities.

Details
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Examples  
Basic Examples  
Scope  
Applications  
Properties & Relations  
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AddSides

AddSides[rel,x]

adds x to each side of the equation or inequality rel.

AddSides[rel1,rel2]

adds the corresponding sides of two equations or inequalities.

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

open all close all

Basic Examples  (3)

Add to both sides of an equation:

Wolfram Language code: AddSides[x - 3 == 7, 3]

Add the corresponding sides of two equations:

Wolfram Language code: AddSides[a == b, c == d]

Add the number to both sides of an inequality:

Wolfram Language code: AddSides[x - b > 7, b]

Scope  (6)

Add to each side of an equation with three expressions:

Wolfram Language code: AddSides[(Sin[a]/a) == (Sin[b]/b) == (Sin[c]/c), r]

Combine an equation and an inequation:

Wolfram Language code: AddSides[a ≠ b, c == d]

Combine an equation and an inequality:

Wolfram Language code: AddSides[z == 7, y > m x + b]

Add to each part of a generalized inequality:

Wolfram Language code: AddSides[a == b > 5 > c, -5]

Add to several inequalities expressed using Piecewise:

Wolfram Language code: AddSides[Piecewise[{{x^2 > c/a + (b*x)/a, a > 0}, {x^2 < c/a + (b*x)/a, a < 0}}, a*x^2 > c + b*x], -x ^ 2]

Add to an equation inside ConditionalExpression:

Wolfram Language code: AddSides[ConditionalExpression[(a/c) == (b/d), c ≠ 0], (-b/d)]

Applications  (1)

Derive the quadratic formula:

Wolfram Language code: quadratic = a x^2 + b x + c == 0

Multiply both sides by :

Wolfram Language code: MultiplySides[quadratic, 4a, Assumptions -> a ≠ 0]//Expand

Add to both sides:

Wolfram Language code: AddSides[%, b^2 - 4a c]

Factor the left-hand side:

Wolfram Language code: Factor[%]

Take the positive square root of both sides:

Wolfram Language code: ApplySides[Sqrt, %]

Cancel the square root of the square:

Wolfram Language code: PowerExpand[%]

Add to both sides:

Wolfram Language code: AddSides[%, -b]

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

Wolfram Language code: DivideSides[%, 2a, Assumptions -> a ≠ 0]

Properties & Relations  (4)

True and False are considered trivial equations:

Wolfram Language code: AddSides[True, a]
Wolfram Language code: AddSides[1 == 0, a]

AddSides transforms equations to equivalent equations:

Wolfram Language code: AddSides[x - 3 == 8, 3]

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

Wolfram Language code: Solve[x - 3 == 8, x]

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

Wolfram Language code: Reduce[x - 3 == 8, x]

Simplify includes the functionality of AddSides:

Wolfram Language code: Simplify[x - 3 == a^2 + 2a b + b^2]
Wolfram Language code: AddSides[x - 3 == a^2 + 2a b + b^2, 3]

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

Wolfram Language code: AddSides[x + y == -5, 5]
Wolfram Language code: SubtractSides[5 + x + y == 0, 5]
Wolfram Research (2018), AddSides, Wolfram Language function, https://reference.wolfram.com/language/ref/AddSides.html.

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2026_addsides, author="Wolfram Research", title="{AddSides}", year="2018", howpublished="\url{https://reference.wolfram.com/language/ref/AddSides.html}", note=[Accessed: 12-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_addsides, organization={Wolfram Research}, title={AddSides}, year={2018}, url={https://reference.wolfram.com/language/ref/AddSides.html}, note=[Accessed: 12-June-2026]}