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>cgeneralized inequalities

Examples

open allclose all

Basic Examples  (4)

Subtract 3 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 x^2 from several inequalities expressed using Piecewise:

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

Applications  (1)

Derive the quadratic formula:

Multiply both sides by 4 a:

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

Factor the left-hand side:

Take the positive square root of both sides:

Cancel the square root of the square:

Subtract b from both sides:

Divide both sides by 2 a to obtain the quadratic formula for x 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]:

Introduced in 2018
 (11.3)