Literal equations
Literal equations
Some equations involve more than one variable. Such equations are called
literal equations .
An equation is solved for a particular variable if that variable alone equals an expression that does not contain that particular variable.
The following equations are examples of literal equations.
-
. It is solved for
.
-
. It is solved for
.
-
. It is solved for
.
-
. It is solved for
.
-
. This equation is not solved for any particular variable since no variable is isolated.
Recall that the equal sign of an equation indicates that the number represented by the expression on the left side is the same as the number represented by the expression on the right side.
This suggests the following procedures:
- We can obtain an equivalent equation (an equation having the same solutions as the original equation) by
adding the
same number to
both sides of the equation.
- We can obtain an equivalent equation by
subtracting the
same number from
both sides of the equation.
We can use these results to isolate
, thus solving for
.
Solving
For
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Solving
For
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Method for solving
And
For
To solve the equation
for
,
subtract
from
both sides of the equation.
To solve the equation
for
,
add
to
both sides of the equation.
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Sample set b
Solve
for
.
Check : Substitute 3 for
in the original equation.
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Solve
for
.
Check : Substitute
for
in the original equation.
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Solve
for
.
On the Calculator
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Solve
for
.
Check : Substitute
for
in the original equation.
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Solve
for
.
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Practice set b
Exercises
For the following problems, classify each of the equations as an identity, contradiction, or conditional equation.
For the following problems, determine which of the literal equations have been solved for a variable. Write "solved" or "not solved."
For the following problems, solve each of the conditional equations.
Exercises for review