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### 10.6 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. See 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 . (see Logical Operations), which converts ‘x = y/3 - 2’ to ‘y/3 - 2’, and s l (see Let Command) which evaluates another formula with ‘x’ set equal to ‘y/3 - 2’.