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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`’.