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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.

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Basic Examples  
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Applications  
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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==rhsequations
    lhs!=rhsinequations
    lhs>rhs or lhs>=rhs inequalities
    ab>c≥…generalized inequalities

Examples

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Basic Examples  (4)

Subtract 3 from both sides of an equation:

Wolfram Language code: SubtractSides[x + 3 == 7, 3]

Subtract the right-hand side of an equation from both sides:

Wolfram Language code: SubtractSides[a + b == c]

Subtract the corresponding sides of two equations:

Wolfram Language code: SubtractSides[a == b, c == d]

Subtract the number b from both sides of an inequality:

Wolfram Language code: SubtractSides[x + b > 7, b]

Scope  (6)

Subtract the rightmost side from each side of an equation with three expressions:

Wolfram Language code: SubtractSides[(Sin[a]/a) == (Sin[b]/b) == (Sin[c]/c)]

Combine an equation and an inequation:

Wolfram Language code: SubtractSides[a ≠ b, c == d]

Combine an equation and an inequality:

Wolfram Language code: SubtractSides[z == 7, y > m x + b]

Subtract from each part of a generalized inequality:

Wolfram Language code: SubtractSides[a == b > -5 > c, -5]

Subtract x^2 from several inequalities expressed using Piecewise:

Wolfram Language code: 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:

Wolfram Language code: SubtractSides[ConditionalExpression[(a/c) == (b/d), c ≠ 0]]

Applications  (1)

Derive the quadratic formula:

Wolfram Language code: quadratic = a x^2 + b x + c == 0

Multiply both sides by 4 a:

Wolfram Language code: MultiplySides[quadratic, 4a, Assumptions -> a ≠ 0]//Expand

Subtract 4 a c-b^2 from both sides:

Wolfram Language code: SubtractSides[%, 4a c - b^2]

Factor the left-hand side:

Wolfram Language code: Factor[%]

Take the positive square root of both sides:

Wolfram Language code: ApplySides[Sqrt, %]

Cancel the square root of the square:

Wolfram Language code: PowerExpand[%]

Subtract b from both sides:

Wolfram Language code: SubtractSides[%, b]

Divide both sides by 2 a to obtain the quadratic formula for x with positive square root:

Wolfram Language code: DivideSides[%, 2a, Assumptions -> a ≠ 0]

Properties & Relations  (4)

True and False are considered trivial equations:

Wolfram Language code: SubtractSides[True, a]
Wolfram Language code: SubtractSides[1 == 0, a]

SubtractSides transforms equations to equivalent equations:

Wolfram Language code: SubtractSides[x + 3 == 8, 3]

Solve gives values for the variables that make the equation true:

Wolfram Language code: Solve[x + 3 == 8, x]

Reduce can be used to rewrite an equation in the form var==value:

Wolfram Language code: Reduce[x + 3 == 8, x]

Simplify includes the functionality of SubtractSides:

Wolfram Language code: Simplify[x - 3 == a^2 + 2a b + b^2]
Wolfram Language code: SubtractSides[x - 3 == a^2 + 2a b + b^2, -3]

SubtractSides[eq,x] is the inverse of AddSides[eq,x]:

Wolfram Language code: SubtractSides[x + y == 5, 5]
Wolfram Language code: AddSides[-5 + x + y == 0, 5]
Wolfram Research (2018), SubtractSides, Wolfram Language function, https://reference.wolfram.com/language/ref/SubtractSides.html.

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: 12-June-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: 12-June-2026]}