How to solve literal equations using the principle of opposites and the I.E.E. method. Calculator: https://www.mathcelebrity.com/literalequation.php

1. Literal Equations (Definition)
A literal equation is an equation which solve for a
variable and the result contains more variables.
Unlike regular equations where the answer is
numeric, literal equation answers contains
variables as well.
Literal Equations are a bedrock of Algebra
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2. Literal Equations Strategy
To succeed solving literal equations, use the
principle of opposites.
To put out fire, firefighters use water
To counteract an acid, you use a base
Isolate the variable to solve for and move
everything else to the other side of the equal sign 2

3. Literal Equation Opposites
Opposites Chart
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Original Operator Original Sign Opposite Operator Opposite Sign
Addition + Subtraction -
Subtraction - Addition +
Multiplication * Division /
Division / Multiplication *
Exponent ^ Root ⺁

4. Literal Equations - Undo Addition
x + y = 2; solve for x
1. Determine everything on the left side of the equation
which is not our variable to solve for
2. For each item, find the opposite operator to eliminate it
3. In this problem, we want to remove (+ y)
4. We need a (- y), since subtraction undoes addition
5. x + y - y = 2 - y
6. x + y - y = 2 - y
7. x = 2 - y
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5. Literal Equations - Undo Subtraction
x - y = 2; solve for x
1. Determine everything on the left side of the equation
which is not our variable to solve for
2. For each item, find the opposite operator to eliminate it
3. In this problem, we want to remove (- y)
4. We need a (+ y), since addition undoes subtraction
5. x - y + y = 2 + y
6. x - y + y = 2 + y
7. x = 2 + y
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6. Literal Equations - Undo Multiplication
A = bh; solve for b
1. Determine everything on the left side of the equation
which is not our variable to solve for
2. For each item, find the opposite operator to eliminate it
3. In this problem, we want to remove (h → *h)
4. We need a (➗h ), since division undoes multiplication
5. A➗h = bh➗h → A➗h = bh➗h
6. b = A➗h or A/h
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7. Literal Equations - Undo Division
A = b/h; solve for b
1. Determine everything on the left side of the equation
which is not our variable to solve for
2. For each item, find the opposite operator to eliminate it
3. In this problem, we want to remove (1/h)
4. We need a (* h ), since multiplication undoes division
undoes
5. A*h = b*h/h → A*h = b*h/h
6. b = Ah
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8. Literal Equations - Undo Exponents
y = x2
; solve for x
1. Determine everything on the left side of the equation
which is not our variable to solve for
2. For each item, find the opposite operator to eliminate it
3. In this problem, we want to remove (2
)
4. We need a (⺁), since roots undo exponents
5. ⺁y = ⺁x2
6. x = ⺁y
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9. Literal Equations - Factoring
Q = 3a + 5ac; solve for a
1. Factor out a
2. Q = a(3 + 5c)
3. Now, we have multiplication, so we undo with division
4. Q/(3 + 5c) = a(3 + 5c)/(3 + 5c)
5. Q/(3 + 5c) = a(3 + 5c)/(3 + 5c)
a = Q/(3 + 5c)
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10. Literal Equations - Conclusion
1. Isolate:
a. Get all terms with the variable you want to solve for to
one side of the equation, either left or right.
2. Eliminate terms using opposites
3. Evaluate
a. Make sure your final answer is simplified
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