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.
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 equationslhs!=rhs inequationslhs>rhs or lhs>=rhs inequalitiesab>c≥… generalized inequalities
- The following options can be given:
-
TimeConstraint 30 time allowed for simplifying conditions
- Possible settings for GenerateConditions include:
-
Automatic return a condition only if it is not generically satisfiedTrue return any condition that is neededFalse never return any needed conditionsNone return unevaluated if conditions are needed
Examples
open all close allBasic Examples (3)
Multiply both sides of an equation by 3:
MultiplySides[x / 3 == 7, 3]Multiply the corresponding sides of two equations:
MultiplySides[a == b, c == d]Multiply both sides of an inequality by the number b:
MultiplySides[x / b > 7, b]Scope (6)
Multiply each side of an equation with three expressions by r:
DivideSides[(Sin[a]/a) == (Sin[b]/b) == (Sin[c]/c), r]Combine an equation and an inequation:
MultiplySides[a ≠ b, c == d]Combine an equation and an inequality:
MultiplySides[y > m x + b, z == 7]Multiply each part of a generalized inequality by :
MultiplySides[a == b > -(1/5) > c, -5]Multiply by a relations expressed using Piecewise :
MultiplySides[Piecewise[{{x^2 == x/a + b, a > 1}, {x^2 <= x/a + b, True}}], a]Multiply by an equation inside ConditionalExpression :
MultiplySides[ConditionalExpression[(a/c) == (b/d), c ≠ 0], (d/b)]Options (3)
Assumptions (1)
Place assumptions on variables to simplify results:
MultiplySides[(x^2/a) > (b /x) + c, a, Assumptions -> a > 0]By default, the different cases will be returned:
MultiplySides[(x^2/a) > (b /x) + c, a]GenerateConditions (2)
The default setting GenerateConditions ->All creates a Piecewise expression if needed:
MultiplySides[a / b > c, b]GenerateConditions ->True returns a valid result with the needed condition:
MultiplySides[a / b > c, b, GenerateConditions -> True]GenerateConditions False returns a valid result without the needed condition:
MultiplySides[a / b > c, b, GenerateConditions -> False]GenerateConditions None will fail if conditions are needed:
MultiplySides[a / b > c, b, GenerateConditions -> None]GenerateConditions ->Automatic returns conditions that are not generically satisfied:
MultiplySides[(a x /b) > 1, b, GenerateConditions -> Automatic]If the condition only fails for a single point, it is not returned:
MultiplySides[(a x /b) == 1, b, GenerateConditions -> Automatic]MultiplySides[(a x /b) == 1, b, GenerateConditions -> True]Applications (1)
Derive the quadratic formula:
quadratic = a x^2 + b x + c == 0Multiply both sides by 4 a:
MultiplySides[quadratic, 4a, Assumptions -> a ≠ 0]//ExpandAdd b^2-4 a c to both sides:
AddSides[%, b^2 - 4a c]Factor the left-hand side:
Factor[%]Take the positive square root of both sides:
ApplySides[Sqrt, %]Cancel the square root of the square:
PowerExpand[%]Subtract b from both sides:
SubtractSides[%, b]Divide both sides by 2 a to obtain the quadratic formula for x with positive square root:
DivideSides[%, 2a, Assumptions -> a ≠ 0]Properties & Relations (5)
True and False are considered trivial equations:
MultiplySides[True, a]MultiplySides[1 == 0, a]MultiplySides transforms equations to equivalent equations:
MultiplySides[x / 3 == 5, 3]Solve gives values for the variables that make the equation true:
Solve[x / 3 == 5, x]Reduce can be used to rewrite an equation in the form var==value:
Reduce[x / 3 == 5, x]Simplify includes the functionality of MultiplySides :
Simplify[2x == 2a b + 4b]MultiplySides[2x == 2a b + 4b, (1/2)]Using Expand to multiply out terms on each side of the equation:
MultiplySides[3x == 15 - 21y, (1/3)]%//ExpandMultiplySides [eq,x] is the inverse of DivideSides [eq,x]:
MultiplySides[(x/2) == y + 24, 2]DivideSides[x == 2 (24 + y), 2]Related Guides
History
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
BibTeX
@misc{reference.wolfram_2026_multiplysides, author="Wolfram Research", title="{MultiplySides}", year="2018", howpublished="\url{https://reference.wolfram.com/language/ref/MultiplySides.html}", note=[Accessed: 15-August-2026]}
BibLaTeX
@online{reference.wolfram_2026_multiplysides, organization={Wolfram Research}, title={MultiplySides}, year={2018}, url={https://reference.wolfram.com/language/ref/MultiplySides.html}, note=[Accessed: 15-August-2026]}