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Solving Literal Equations
Solving a literal equation follows the same rules as solving a linear equation. So what is a literal equation and how do you solve them? A literal equation differs from other equations because you are not solving for a specific value for a specific variable. For example, many times you are looking for a value for x that will make an equation true. In a literal equation, you are simply rearranging variables into a more convenient form so that you can plug in values for variables later. Literal equations are usually formulas that are used in some type of application. For example, area, force, volume, and distance formulas can all be a starting point of a literal equation.

Suppose you have the area formula for a rectangle, . When working with literal equations, you have to be given an additional piece of information other than simply being given a formula. You have to be told what variable you will be solving for. The way the equation is originally presented, we say that the equation is solved for A. In certain situations it might be helpful to have the equation solved for l. So the task is to solve for l. As mentioned earlier, this will involve the same skills needed to solve a linear equation. To review solving linear equations, click here (linear equations solving.doc) In this case, you only need to divide both sides by w to have .

You may be asking yourself why you would want to have the equation solved for a different variable. If you are given the area and the width and asked to find the length, you now have a formula already solved for length. As formulas become more complicated, many times it is useful to have the equation solved for a different variable so you can go straight to plugging in values that you know and solving for the value you do not know.

Let's Practice:
  1. Solve for b. This is the formula for the area of a triangle.
As with the problem shown earlier, this equation is solved for A. To solve for b, you should start by multiplying both sides by 2 to get rid of the fraction. Now to have b by itself, divide by sides by h.
Notice that you can be given this equation and asked to solve either for b or for h. That’s why it is absolutely necessary to be told which variable you are solving for.
  1. Solve for h. This is the formula for the volume of a cylinder.
To solve for h, you will need to divide both sides by and .
This problem would require a little more work if you were asked to solve for r. You would need to take a square root to find your answer. You can check your answer after working the first problem in the Examples section below.

Examples
Example
Solve for r.
What is your answer?
 
Example Solve for h.
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Example Solve for .
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Example Solve for C.
What is your answer?
 
Example Solve for a.
What is your answer?
 
Example Solve for t.
What is your answer?
 
Example Solve for .
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Example Solve for G.
What is your answer?
 
Example
What is your answer?
 



S Taylor

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