# ApplySides

ApplySides[f,rel]

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

# Details • The relations rel can have any of the following forms:
•  lhs==rhs equations lhs!=rhs inequations lhs>rhs or lhs>=rhs inequalities ab>c≥… generalized inequalities
• ApplySides does not verify that inequalities are still valid after function application.

# Examples

open allclose all

## 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)

Multiply both sides by :

Add to both sides:

Factor the left-hand side:

Take the positive square root of both sides:

Cancel the square root of the square:

Subtract from both sides:

Divide both sides by to obtain the quadratic formula for 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: