AddSides

AddSides[rel,x]

adds x to each side of the equation or inequality rel.

AddSides[rel1,rel2]

adds the corresponding sides of two equations or inequalities.

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  (3)

Add to both sides of an equation:

Add the corresponding sides of two equations:

Add the number to both sides of an inequality:

Scope  (6)

Add to each side of an equation with three expressions:

Combine an equation and an inequation:

Combine an equation and an inequality:

Add to each part of a generalized inequality:

Add to several inequalities expressed using Piecewise:

Add to an equation inside ConditionalExpression:

Applications  (1)

Derive the quadratic formula:

Multiply both sides by :

Add to both sides:

Factor the left-hand side:

Take the positive square root of both sides:

Cancel the square root of the square:

Add to 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:

AddSides 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 AddSides:

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

Introduced in 2018
 (11.3)