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 ab>c≥… generalized inequalities - The following options can be given:
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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:
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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 all close allBasic Examples (3)
: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)
GenerateConditions (2)
The default setting GenerateConditions->All creates a Piecewise expression if needed:
GenerateConditions->True returns a valid result with the needed condition:
GenerateConditionsFalse returns a valid result without the needed condition:
GenerateConditionsNone will fail if conditions are needed:
GenerateConditions->Automatic returns conditions that are not generically satisfied:
If the condition only fails for a single point, it is not returned:
Applications (1)
:
to both sides:
from both sides:
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]:
Text
Wolfram Research (2018), MultiplySides, Wolfram Language function, https://reference.wolfram.com/language/ref/MultiplySides.html.
CMS
Wolfram Language. 2018. "MultiplySides." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/MultiplySides.html.
APA
Wolfram Language. (2018). MultiplySides. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/MultiplySides.html