Exponentiate both sides of an equation:

Take the square root of both sides of an inequality:

Compute the logarithm of each side of an equation with three expressions:

Take the cube root of each side of a generalized inequality:

Apply Factorial to both sides of an inequation:

Raise each side of an equation to the fourth power using a pure function:

Apply Sinh to several inequalities expressed using Piecewise:

Compute the common logarithm of both sides of an equation inside ConditionalExpression:

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:

Subtract from both sides:

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

True and False are considered trivial equations:

ApplySides transforms equations to related 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:

ApplySides is a purely structural operation and does not check mathematical consistency:

The new inequality is not equivalent to the original: