# 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 equations lhs!=rhs inequations lhs>rhs or lhs>=rhs inequalities ab>c≥… generalized inequalities

# Examples

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## Basic Examples(4)

Subtract from both sides of an equation:

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

Subtract the corresponding sides of two equations:

Subtract the number b from both sides of an inequality:

## Scope(6)

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

Combine an equation and an inequation:

Combine an equation and an inequality:

Subtract from each part of a generalized inequality:

Subtract from several inequalities expressed using Piecewise:

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

## Applications(1)

Multiply both sides by :

Subtract from both sides:

Factor the left-hand side:

Take the positive square root of both sides:

Cancel the square root of the square:

Subtract from both sides:

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

## Properties & Relations(4)

True and False are considered trivial equations:

SubtractSides 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 SubtractSides:

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