Solving Literal Equations

Literal equations are equations with multiple letters in them as variables. X = 3(7)+4 is an equation that can be solved to a single answer, but X = 3Y+Q is a literal equation because it cannot be solved that way. Instead, there are letters in the answer.

The algebra is exactly the same, though, whether you are solving literal equations or standard equations.

Example 1: Solve PV = nRT for n.

Our goal is to isolate n. Since it is currently being multiplied by RT, we can divide both sides by RT to get n by itself.

Note that the variable we are solving for can be on the right side of the equation. (We often have it on the left, but if A = B, then B=A, so in this case if PV/RT = n then n=PV/RT and we do not need to waste time or effort moving the desired variable to the left hand side of the equation.

In the case of solving for something that is got more going on with that side of the equation, I recommend the reverse of order of operations. Since you normally do parentheses/exponents first with numbers and addition/subtraction last, you will reverse that order and do any addition and subtraction first and end with exponents and parentheses. This is not the only way to do it, but it can help if you are unsure of how to start.

Example 2: To be continued

Remember that sin, cos & tangent are undone by taking the inverse of that function.

Example 3: