({{, (RefLink[AddSides, paclet:ref/AddSides])[rel,x] 
adds x to each side of the equation or inequality rel.}, {, (RefLink[AddSides, paclet:ref/AddSides])[(Subscript[rel, 1]),(Subscript[rel, 2])]
adds the corresponding sides of two equations or inequalities.}})

OpenersNotesSection(Spacer1)Details

The relations rel can have any of the following forms:

OpenersPrimaryExamplesSection(Spacer1)Examples  (14)

OpenersExampleSection0(Spacer1)Basic Examples  (3)

Add 3 to both sides of an equation:

AddSides[x-3==7,3]

Add the corresponding sides of two equations:

AddSides[a==b,c==d]

Add the number b to both sides of an inequality:

AddSides[x-b>7,b]

OpenersExampleSection1(Spacer1)Scope  (6)

Add r to each side of an equation with three expressions:

AddSides[((Sin[a])/a)==((Sin[b])/b)==((Sin[c])/c),r]

Combine an equation and an inequation:

AddSides[a≠b,c==d]

Combine an equation and an inequality:

AddSides[z==7,y>m x+b]

Add -5 to each part of a generalized inequality:

AddSides[a==b>5>c,-5]

Add -(x^2) to several inequalities expressed using (RefLink[Piecewise, paclet:ref/Piecewise]):

AddSides[({{\[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, True}})}}),-x^2]

Add -(b/d) to an equation inside (RefLink[ConditionalExpression, paclet:ref/ConditionalExpression]):

AddSides[ConditionalExpression[(a/c)==(b/d),c≠0],((-b)/d)]

OpenersExampleSection3(Spacer1)Applications  (1)

Derive the quadratic formula:

quadratic=a (x^2)+b x + c==0

Multiply both sides by 4 a:

MultiplySides[quadratic,4a,Assumptions->a≠0]//Expand

Add (b^2)-4 a c to both sides:

AddSides[%,(b^2)-4a c]

Factor the left-hand side:

Factor[%]

Take the positive square root of both sides:

ApplySides[Sqrt,%]

Cancel the square root of the square:

PowerExpand[%]

Add -b to both sides:

AddSides[%, -b]

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

DivideSides[%,2a,Assumptions->a≠0]

OpenersExampleSection4(Spacer1)Properties & Relations  (4)

(RefLink[True, paclet:ref/True]) and (RefLink[False, paclet:ref/False]) are considered trivial equations:

AddSides[True,a]

AddSides[1==0,a]

(RefLink[AddSides, paclet:ref/AddSides]) transforms equations to equivalent equations:

AddSides[x-3==8,3]

(RefLink[Solve, paclet:ref/Solve]) gives values for the variables that make the equation true:

Solve[x-3==8,x]

(RefLink[Reduce, paclet:ref/Reduce]) can be used to rewrite an equation in the form var==value:

Reduce[x-3==8,x]

(RefLink[Simplify, paclet:ref/Simplify]) includes the functionality of (RefLink[AddSides, paclet:ref/AddSides]):

Simplify[x-3==(a^2)+2a b + (b^2)]

AddSides[x-3==(a^2)+2a b + (b^2),3]

(RefLink[AddSides, paclet:ref/AddSides])[eq,x] is the inverse of (RefLink[SubtractSides, paclet:ref/SubtractSides])[eq,x]:

AddSides[x+y==-5,5]

SubtractSides[5+x+y==0,5]

({{DocumentationFooterIconsRelatedFunction.png, ({{See Also}, {(RefLink[SubtractSides, paclet:ref/SubtractSides])  ▪  (RefLink[MultiplySides, paclet:ref/MultiplySides])  ▪  (RefLink[DivideSides, paclet:ref/DivideSides])  ▪  (RefLink[Solve, paclet:ref/Solve])  ▪  (RefLink[Reduce, paclet:ref/Reduce])  ▪  (RefLink[ApplySides, paclet:ref/ApplySides])  ▪  (RefLink[Simplify, paclet:ref/Simplify])  ▪  (RefLink[Factor, paclet:ref/Factor])}})}})

({{DocumentationFooterIconsRelatedGuide.png, ({{Related Guides}, {▪(RefLinkPlain[Manipulating Equations, paclet:guide/ManipulatingEquations])}, {▪(RefLinkPlain[Formula Manipulation, paclet:guide/FormulaManipulation])}, {▪(RefLinkPlain[Precollege Education, paclet:guide/PrecollegeEducation])}})}})