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Finite Math Examples
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Step 1
Step 1.1
Simplify each term.
Step 1.1.1
Combine and .
Step 1.1.2
Combine and .
Step 1.1.3
Move to the left of .
Step 1.2
Add to both sides of the equation.
Step 1.3
Multiply both sides of the equation by .
Step 1.4
Simplify both sides of the equation.
Step 1.4.1
Simplify the left side.
Step 1.4.1.1
Simplify .
Step 1.4.1.1.1
Cancel the common factor of .
Step 1.4.1.1.1.1
Cancel the common factor.
Step 1.4.1.1.1.2
Rewrite the expression.
Step 1.4.1.1.2
Cancel the common factor of .
Step 1.4.1.1.2.1
Factor out of .
Step 1.4.1.1.2.2
Cancel the common factor.
Step 1.4.1.1.2.3
Rewrite the expression.
Step 1.4.2
Simplify the right side.
Step 1.4.2.1
Simplify .
Step 1.4.2.1.1
Apply the distributive property.
Step 1.4.2.1.2
Multiply .
Step 1.4.2.1.2.1
Combine and .
Step 1.4.2.1.2.2
Multiply by .
Step 1.4.2.1.3
Cancel the common factor of .
Step 1.4.2.1.3.1
Factor out of .
Step 1.4.2.1.3.2
Cancel the common factor.
Step 1.4.2.1.3.3
Rewrite the expression.
Step 1.4.2.1.4
Combine and .
Step 1.4.2.1.5
Multiply by .
Step 1.4.2.1.6
Combine and .
Step 1.5
Reorder and .
Step 2
Step 2.1
Replace all occurrences of in with .
Step 2.2
Simplify the left side.
Step 2.2.1
Simplify .
Step 2.2.1.1
Simplify each term.
Step 2.2.1.1.1
Apply the distributive property.
Step 2.2.1.1.2
Cancel the common factor of .
Step 2.2.1.1.2.1
Factor out of .
Step 2.2.1.1.2.2
Factor out of .
Step 2.2.1.1.2.3
Cancel the common factor.
Step 2.2.1.1.2.4
Rewrite the expression.
Step 2.2.1.1.3
Multiply by .
Step 2.2.1.1.4
Multiply by .
Step 2.2.1.1.5
Cancel the common factor of .
Step 2.2.1.1.5.1
Factor out of .
Step 2.2.1.1.5.2
Cancel the common factor.
Step 2.2.1.1.5.3
Rewrite the expression.
Step 2.2.1.1.6
Combine and .
Step 2.2.1.2
To write as a fraction with a common denominator, multiply by .
Step 2.2.1.3
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Step 2.2.1.3.1
Multiply by .
Step 2.2.1.3.2
Multiply by .
Step 2.2.1.4
Combine the numerators over the common denominator.
Step 2.2.1.5
Simplify each term.
Step 2.2.1.5.1
Simplify the numerator.
Step 2.2.1.5.1.1
Factor out of .
Step 2.2.1.5.1.1.1
Factor out of .
Step 2.2.1.5.1.1.2
Factor out of .
Step 2.2.1.5.1.1.3
Factor out of .
Step 2.2.1.5.1.2
Multiply by .
Step 2.2.1.5.1.3
Add and .
Step 2.2.1.5.2
Cancel the common factor of and .
Step 2.2.1.5.2.1
Factor out of .
Step 2.2.1.5.2.2
Cancel the common factors.
Step 2.2.1.5.2.2.1
Factor out of .
Step 2.2.1.5.2.2.2
Cancel the common factor.
Step 2.2.1.5.2.2.3
Rewrite the expression.
Step 2.2.1.5.3
Move to the left of .
Step 3
Step 3.1
Move all terms not containing to the right side of the equation.
Step 3.1.1
Subtract from both sides of the equation.
Step 3.1.2
To write as a fraction with a common denominator, multiply by .
Step 3.1.3
Combine and .
Step 3.1.4
Combine the numerators over the common denominator.
Step 3.1.5
Simplify the numerator.
Step 3.1.5.1
Multiply by .
Step 3.1.5.2
Subtract from .
Step 3.2
Since the expression on each side of the equation has the same denominator, the numerators must be equal.
Step 3.3
Divide each term in by and simplify.
Step 3.3.1
Divide each term in by .
Step 3.3.2
Simplify the left side.
Step 3.3.2.1
Cancel the common factor of .
Step 3.3.2.1.1
Cancel the common factor.
Step 3.3.2.1.2
Divide by .
Step 3.3.3
Simplify the right side.
Step 3.3.3.1
Divide by .
Step 4
Step 4.1
Replace all occurrences of in with .
Step 4.2
Simplify the right side.
Step 4.2.1
Simplify .
Step 4.2.1.1
Combine the numerators over the common denominator.
Step 4.2.1.2
Simplify the expression.
Step 4.2.1.2.1
Multiply by .
Step 4.2.1.2.2
Add and .
Step 4.2.1.2.3
Divide by .
Step 5
The solution to the system is the complete set of ordered pairs that are valid solutions.
Step 6
The result can be shown in multiple forms.
Point Form:
Equation Form:
Step 7