SubtractSides [rel,x]
subtracts x from each side of the equation or inequality rel.
SubtractSides [rel1,rel2]
subtracts the corresponding sides of two equations or inequalities.
SubtractSides [rel]
subtracts the right-hand side of rel from each side, producing a zero right-hand side.
SubtractSides
SubtractSides [rel,x]
subtracts x from each side of the equation or inequality rel.
SubtractSides [rel1,rel2]
subtracts the corresponding sides of two equations or inequalities.
SubtractSides [rel]
subtracts the right-hand side of rel from each side, producing a zero right-hand side.
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 (4)
Subtract 3 from both sides of an equation:
SubtractSides[x + 3 == 7, 3]Subtract the right-hand side of an equation from both sides:
SubtractSides[a + b == c]Subtract the corresponding sides of two equations:
SubtractSides[a == b, c == d]Subtract the number b from both sides of an inequality:
SubtractSides[x + b > 7, b]Scope (6)
Subtract the rightmost side from each side of an equation with three expressions:
SubtractSides[(Sin[a]/a) == (Sin[b]/b) == (Sin[c]/c)]Combine an equation and an inequation:
SubtractSides[a ≠ b, c == d]Combine an equation and an inequality:
SubtractSides[z == 7, y > m x + b]Subtract from each part of a generalized inequality:
SubtractSides[a == b > -5 > c, -5]Subtract x^2 from several inequalities expressed using Piecewise :
SubtractSides[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]Subtract the right-hand side from both sides of an equation inside ConditionalExpression :
SubtractSides[ConditionalExpression[(a/c) == (b/d), c ≠ 0]]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]//ExpandSubtract 4 a c-b^2 from both sides:
SubtractSides[%, 4a c - b^2]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 (4)
True and False are considered trivial equations:
SubtractSides[True, a]SubtractSides[1 == 0, a]SubtractSides transforms equations to equivalent equations:
SubtractSides[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 SubtractSides :
Simplify[x - 3 == a^2 + 2a b + b^2]SubtractSides[x - 3 == a^2 + 2a b + b^2, -3]SubtractSides [eq,x] is the inverse of AddSides [eq,x]:
SubtractSides[x + y == 5, 5]AddSides[-5 + x + y == 0, 5]Related Guides
History
Text
Wolfram Research (2018), SubtractSides, Wolfram Language function, https://reference.wolfram.com/language/ref/SubtractSides.html.
CMS
Wolfram Language. 2018. "SubtractSides." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/SubtractSides.html.
APA
Wolfram Language. (2018). SubtractSides. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SubtractSides.html
BibTeX
@misc{reference.wolfram_2026_subtractsides, author="Wolfram Research", title="{SubtractSides}", year="2018", howpublished="\url{https://reference.wolfram.com/language/ref/SubtractSides.html}", note=[Accessed: 16-August-2026]}
BibLaTeX
@online{reference.wolfram_2026_subtractsides, organization={Wolfram Research}, title={SubtractSides}, year={2018}, url={https://reference.wolfram.com/language/ref/SubtractSides.html}, note=[Accessed: 16-August-2026]}