applies f to each side of the equation or inequality rel.


  • The relations rel can have any of the following forms:
  • lhs==rhsequations
    lhs>rhs or lhs>=rhs inequalities
    ab>cgeneralized inequalities
  • ApplySides does not verify that inequalities are still valid after function application.


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Basic Examples  (2)

Exponentiate both sides of an equation:

Take the square root of both sides of an inequality:

Scope  (6)

Compute the logarithm of each side of an equation with three expressions:

Take the cube root of each side of a generalized inequality:

Apply Factorial to both sides of an inequation:

Raise each side of an equation to the fourth power using a pure function:

Apply Sinh to several inequalities expressed using Piecewise:

Compute the common logarithm of both sides of an equation inside ConditionalExpression:

Applications  (1)

Derive the quadratic formula:

Multiply both sides by 4 a:

Add b^2-4 a c to both sides:

Factor the left-hand side:

Take the positive square root of both sides:

Cancel the square root of the square:

Subtract b from both sides:

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

Properties & Relations  (2)

True and False are considered trivial equations:

ApplySides transforms equations to related equations:

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

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

Possible Issues  (1)

ApplySides is a purely structural operation and does not check mathematical consistency:

The new inequality is not equivalent to the original:

Wolfram Research (2018), ApplySides, Wolfram Language function,


Wolfram Research (2018), ApplySides, Wolfram Language function,


Wolfram Language. 2018. "ApplySides." Wolfram Language & System Documentation Center. Wolfram Research.


Wolfram Language. (2018). ApplySides. Wolfram Language & System Documentation Center. Retrieved from


@misc{reference.wolfram_2024_applysides, author="Wolfram Research", title="{ApplySides}", year="2018", howpublished="\url{}", note=[Accessed: 20-July-2024 ]}


@online{reference.wolfram_2024_applysides, organization={Wolfram Research}, title={ApplySides}, year={2018}, url={}, note=[Accessed: 20-July-2024 ]}