# MultiplySides

MultiplySides[rel,x]

multiplies each side of the equation or inequality rel by x.

MultiplySides[rel1,rel2]

multiplies the corresponding sides of two equations or inequalities.

# Details and Options • 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
• The following options can be given:
•  Assumptions \$Assumptions assumptions on parameters GenerateConditions All whether to generate conditions on parameters TimeConstraint 30 time allowed for simplifying conditions
• Possible settings for GenerateConditions include:
•  All return all possible answers using Piecewise Automatic return a condition only if it is not generically satisfied True return any condition that is needed False never return any needed conditions None return unevaluated if conditions are needed

# Examples

open allclose all

## Basic Examples(3)

Multiply both sides of an equation by 3:

Multiply the corresponding sides of two equations:

Multiply both sides of an inequality by the number :

## Scope(6)

Multiply each side of an equation with three expressions by r:

Combine an equation and an inequation:

Combine an equation and an inequality:

Multiply each part of a generalized inequality by :

Multiply by relations expressed using Piecewise:

Multiply by an equation inside ConditionalExpression:

## Options(3)

### Assumptions(1)

Place assumptions on variables to simplify results:

By default, the different cases will be returned:

### GenerateConditions(2)

The default setting creates a Piecewise expression if needed:

returns a valid result with the needed condition:

returns a valid result without the needed condition:

will fail if conditions are needed:

returns conditions that are not generically satisfied:

If the condition only fails for a single point, it is not returned:

## 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(5)

True and False are considered trivial equations:

MultiplySides transforms equations to equivalent 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:

Simplify includes the functionality of MultiplySides:

Using Expand to multiply out terms on each side of the equation:

MultiplySides[eq,x] is the inverse of DivideSides[eq,x]: