Literal Equations
A literal equation is an equation that has more than one variable.
For instance, 3a + 7b = 10 is a literal equation because it has two variables, a and b. Formulas such as the circumference of a circle, C = ∏r, are really literal equations.
You have heard that work "literal" before in literacy, literature, and literary. It comes from the Latin word for "letter." In a literal equation we are asked to solve for one of the variables. A literal equation is an equation that has more than one variable. For instance, 3a + 7b = 10 is a literal equation because it has two variables, a and b. Formulas such as the circumference of a circle, C = ∏r, are really literal equations. You have heard that work "literal" before in literacy, literature, and literary. It comes from the Latin word for "letter." In a literal equation we are asked to solve for one of the variables.
Example #1
Solve for b in the given equation.
3a + 7b = 10
-3a = -3a
7b = 10-3a
Subtract 3a from each side. Then divide each side by 7.
Example #2
Solve for a in the given equation.
3a + 7b = 10
-7b = -7b
3a = 10-7b
Substract 7b from each side, then divide each side by 3.
Example #3
Solve for r in the given equation.
C = 2πr
Divide each side by 2∏, then use symmetric propergy of equality.
Example #4
Solve for a in the given quations.
a2 + b2 = c2
a2 = b2 - c2
Notice the ± in front of the radical. Remember that there are always two solutions when we take the square root to solve an equation. Of course if this equation is using the Pythagorean Theorem and a, b, and c represent the lengths of sides in a right triangle, then we won't need the negative sign because length is always positive.
Example #5
Solve for b2 in the given equation.
On both sides, multiply by 2 and divide by h.
Subtract b2 from both sides, and then then use summetric Property of Equality.
