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The concept of literal equations and formulas, focusing on the perimeter of a rectangle as an example. It also provides two examples of solving literal equations for different variables using algebraic methods. Students will learn how to identify the variable they want to have alone, treat all other letters as numbers, and apply the rules of algebra to solve the equations.
What you will learn
Typology: Summaries
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Literal Equations & Formula
A literal equation is an equation which consists primarily of letters. Formulas are an example of literal equations. Each variable in the equation "literally" represents an important part of the whole relationship expressed by the equation.
For example,
The perimeter of a rectangle is expressed as P = 2L + 2W
The "L" represents the length of one side of the rectangle. We see "2L" in the formula since there are two sides in a rectangle. The "W" represents the measure of the width. There is a "width" at opposite ends of the rectangle, hence "2W".
Solving Literal Equations
To solve a literal equation means to rewrite the equation so a different variable stands alone on one side of the equals sign. We have to be told for which variable we want to solve.
For example,
If we were asked to solve the equation P = 2W + 2L for W, we would get W = ( P - 2L ) / 2
We started with " P = ..." and ended with " W = ... ". That's what it means to "solve a literal equation."
Method:
Example 1:
Solve 5x + 2y = 7 for "y".
Solution:
5x + 2 y = 7 Identify "y" as the variable you want alone. 5x -5x + 2 y = 7 - 5x Add the opposite of 5x to both sides. 2 y = 7 - 5x 2 y = 7 - 5x Divide all terms on both sides by the coefficient of "y" 2 2 2
y = 7 - 5x Here is your solution. 2 2
Rewritten for "y": y = ( 7/2 ) - ( 5/2 )x
Example 2:
Solve T = 2 ππ R(R+h) for h
Solution:
T = 2 πR( R + h ) Identify "h" as the variable you want alone.
T = 2 πR( R + h ) Divide both sides by the factors 2πR. 2 πR 2 πR
T = 2 πR( R + h ) Cancel. 2 πR 2 πR
T = ( R + h ) To solve for h, add the opposite of R to both sides. 2 πR
T - R = R + h - R 2 πR
T - R = h You are done. 2 πR
Hence, h = [ T / ( 2 ππ R ) ] - R