calc: Solving Equations
11.6 Solving Equations
======================
The ‘a S’ (‘calc-solve-for’) [‘solve’] command rearranges an equation to
solve for a specific variable. An equation is an expression of the form
‘L = R’. For example, the command ‘a S x’ will rearrange ‘y = 3x + 6’
to the form, ‘x = y/3 - 2’. If the input is not an equation, it is
treated like an equation of the form ‘X = 0’.
This command also works for inequalities, as in ‘y < 3x + 6’. Some
inequalities cannot be solved where the analogous equation could be; for
example, solving ‘a < b c’ for ‘b’ is impossible without knowing the
sign of ‘c’. In this case, ‘a S’ will produce the result ‘b != a/c’
(using the not-equal-to operator) to signify that the direction of the
inequality is now unknown. The inequality ‘a <= b c’ is not even
partially solved. 
Declarations, for a way to tell Calc that the
signs of the variables in a formula are in fact known.
Two useful commands for working with the result of ‘a S’ are ‘a .’
(Logical Operations), which converts ‘x = y/3 - 2’ to ‘y/3 - 2’,
and ‘s l’ (Let Command) which evaluates another formula with ‘x’
set equal to ‘y/3 - 2’.
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