AddSides
Details
- The relations rel can have any of the following forms:
-
lhs==rhs equationslhs!=rhs inequationslhs>rhs or lhs>=rhs inequalitiesab>c≥… generalized inequalities
Examples
open all close allBasic Examples (3)
Add to both sides of an equation:
AddSides[x - 3 == 7, 3]Add the corresponding sides of two equations:
AddSides[a == b, c == d]Add the number to both sides of an inequality:
AddSides[x - b > 7, b]Scope (6)
Add to each side of an equation with three expressions:
AddSides[(Sin[a]/a) == (Sin[b]/b) == (Sin[c]/c), r]Combine an equation and an inequation:
AddSides[a ≠ b, c == d]Combine an equation and an inequality:
AddSides[z == 7, y > m x + b]Add to each part of a generalized inequality:
AddSides[a == b > 5 > c, -5]Add to several inequalities expressed using Piecewise :
AddSides[Piecewise[{{x^2 > c/a + (b*x)/a, a > 0}, {x^2 < c/a + (b*x)/a, a < 0}}, a*x^2 > c + b*x], -x ^ 2]Add to an equation inside ConditionalExpression :
AddSides[ConditionalExpression[(a/c) == (b/d), c ≠ 0], (-b/d)]Applications (1)
Derive the quadratic formula:
quadratic = a x^2 + b x + c == 0Multiply both sides by :
MultiplySides[quadratic, 4a, Assumptions -> a ≠ 0]//ExpandAdd 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[%]Add to both sides:
AddSides[%, -b]Divide both sides by to obtain the quadratic formula for with positive square root:
DivideSides[%, 2a, Assumptions -> a ≠ 0]Properties & Relations (4)
True and False are considered trivial equations:
AddSides[True, a]AddSides[1 == 0, a]AddSides transforms equations to equivalent equations:
AddSides[x - 3 == 8, 3]Solve gives values for the variables that make the equation true:
Solve[x - 3 == 8, x]Reduce can be used to rewrite an equation in the form var==value:
Reduce[x - 3 == 8, x]Simplify includes the functionality of AddSides :
Simplify[x - 3 == a^2 + 2a b + b^2]AddSides[x - 3 == a^2 + 2a b + b^2, 3]AddSides [eq,x] is the inverse of SubtractSides [eq,x]:
AddSides[x + y == -5, 5]SubtractSides[5 + x + y == 0, 5]Related Guides
History
Text
Wolfram Research (2018), AddSides, Wolfram Language function, https://reference.wolfram.com/language/ref/AddSides.html.
CMS
Wolfram Language. 2018. "AddSides." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/AddSides.html.
APA
Wolfram Language. (2018). AddSides. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/AddSides.html
BibTeX
@misc{reference.wolfram_2026_addsides, author="Wolfram Research", title="{AddSides}", year="2018", howpublished="\url{https://reference.wolfram.com/language/ref/AddSides.html}", note=[Accessed: 14-August-2026]}
BibLaTeX
@online{reference.wolfram_2026_addsides, organization={Wolfram Research}, title={AddSides}, year={2018}, url={https://reference.wolfram.com/language/ref/AddSides.html}, note=[Accessed: 14-August-2026]}