Literal Equations

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Literal Equations
Practice
Foundations of Algebra
Step 1. Start with an example. It could be an equation
or a formula.
Step 2. Identify the target variable. The first thing you
need to do is identify what variable you are solving for,
or your target variable. Your goal is to get all the letters
in your equation on one side of the equation, and your
target variable, by itself, on the other side of the
equation.
Step 3. Remember the order of operations.
When solving literal equations, the order of operations is as
follows: Exponents and roots, multiplication and division,
addition and subtraction. When moving variables from
one side of an equation to another you will perform the
order of operations backwards: Subtraction, Addition,
Division, Multiplication, Exponents, Parentheses.
Step 4. Move the letters. Move all the letters to one side of
the equation, leaving your target variable isolated. When
doing this be careful that you follow reverse order of
operations: Subtraction, Addition, Division, Multiplication,
Exponents, Parentheses.

Step 5. Solve for the target variable. You are done
when target variable is isolated. Keep in mind that
due to all the variables, you will not be able to
simplify your equations as much as you are used to
in linear algebra. When your target variable is
isolated on one side of the equation, with all the
other variables on the other side, you are done.
Example 1: Application
The formula C = d gives the circumference of a circle
C in terms of diameter d. The circumference of a bowl
is 18 inches. What is the bowl's diameter? Leave the
symbol  in your answer.
Locate d in the equation.
Since d is multiplied by , divide both
sides by  to undo the multiplication.
Now use this formula and the information given in the
problem.
Example 1: Application Continued
The formula C = d gives the circumference of a circle
C in terms of diameter d. The circumference of a bowl
is 18 inches. What is the bowl's diameter? Leave the
symbol  in your answer.
Now use this formula and the information given in the
problem.
The bowl's diameter is
I inches.
Example 2: the distance formula
Solve the formula d = rt for t. Find the time in hours that
it would take Zach to travel 26.2 miles if his average
speed was 18 miles per hour.
d = rt
Locate t in the equation.
Since t is multiplied by r, divide
both sides by r to undo the
multiplication.
Now use this formula and the information given in the
problem.
Example 2 continued…
Solve the formula d = rt for t. Find the time in hours that
it would take Zach to travel 26.2 miles if his average
speed was 18 miles per hour.
Zach’s time was about 1.46 hours.
Example 3: Area of a Triangle Formula
The formula for the area of a triangle is A = bh,
where b is the length of the base, and is the height. Solve
for h.
A=
bh
2A = bh
Locate h in the equation.
Since bh is multiplied by , divide
both sides by to undo the
multiplication.
Since h is multiplied by b, divide
both sides by b to undo the
multiplication.

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