Technical Mathematics, Sixth Edition

11.10. Literal Equations and Formulas

A literal equation is one in which some or all of the constants are represented by letters.

Example 65: The following is a literal equation: a(x + b) = b(x + c)

A formula is a literal equation that relates two or more mathematical or physical quantities. These are the equations that describe the workings of the physical world. In Chap. 1 we substituted into formulas. Here we solve formulas or other literal equations for one of its quantities.

11.10.1. Solving Literal Equations and Formulas

When we solve a literal equation or formula, we cannot, of course, get a numerical answer, as we could with a numerical equation. Our object here is to isolate one of the letters on one side of the equal sign. We "solve for" one of the literal quantities.

Example 66: Solve for x: a(x + b) = b(x + c) Solution: Our goal is to isolate x on one side of the equation. Removing parentheses, we obtain ax + ab = bx + bc Subtracting bx and then ab will place all of the x terms on one side of the equation. ax − bx = bc − ab Factoring to isolate x yields x(a − b) = b(c − a) Dividing by (a − b), where a ≠ b, gives us Check: We substitute our answer into our original equation.

We solve literal equations by calculator in the same way we solved numerical equations. Select ...