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Finite Math Examples
, ,
Step 1
Step 1.1
Subtract from both sides of the equation.
Step 1.2
Subtract from both sides of the equation.
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
Simplify.
Step 2.2.1.1.2.1
Multiply by .
Step 2.2.1.1.2.2
Multiply by .
Step 2.2.1.1.2.3
Multiply by .
Step 2.2.1.2
Simplify by adding terms.
Step 2.2.1.2.1
Add and .
Step 2.2.1.2.2
Add and .
Step 2.3
Replace all occurrences of in with .
Step 2.4
Simplify the left side.
Step 2.4.1
Subtract from .
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
Add to both sides of the equation.
Step 3.2
Divide each term in by and simplify.
Step 3.2.1
Divide each term in by .
Step 3.2.2
Simplify the left side.
Step 3.2.2.1
Cancel the common factor of .
Step 3.2.2.1.1
Cancel the common factor.
Step 3.2.2.1.2
Divide by .
Step 3.2.3
Simplify the right side.
Step 3.2.3.1
Simplify each term.
Step 3.2.3.1.1
Dividing two negative values results in a positive value.
Step 3.2.3.1.2
Move the negative in front of the fraction.
Step 4
Step 4.1
Replace all occurrences of in with .
Step 4.2
Simplify the left side.
Step 4.2.1
Simplify .
Step 4.2.1.1
Simplify each term.
Step 4.2.1.1.1
Apply the distributive property.
Step 4.2.1.1.2
Multiply .
Step 4.2.1.1.2.1
Combine and .
Step 4.2.1.1.2.2
Multiply by .
Step 4.2.1.1.3
Multiply .
Step 4.2.1.1.3.1
Multiply by .
Step 4.2.1.1.3.2
Combine and .
Step 4.2.1.1.4
Move the negative in front of the fraction.
Step 4.2.1.2
To write as a fraction with a common denominator, multiply by .
Step 4.2.1.3
Combine and .
Step 4.2.1.4
Combine the numerators over the common denominator.
Step 4.2.1.5
Simplify the numerator.
Step 4.2.1.5.1
Multiply by .
Step 4.2.1.5.2
Add and .
Step 4.2.1.6
To write as a fraction with a common denominator, multiply by .
Step 4.2.1.7
Combine and .
Step 4.2.1.8
Combine the numerators over the common denominator.
Step 4.2.1.9
Combine the numerators over the common denominator.
Step 4.2.1.10
Multiply by .
Step 4.2.1.11
Add and .
Step 4.2.1.12
Factor out of .
Step 4.2.1.12.1
Factor out of .
Step 4.2.1.12.2
Factor out of .
Step 4.3
Replace all occurrences of in with .
Step 4.4
Simplify the right side.
Step 4.4.1
Simplify .
Step 4.4.1.1
Simplify each term.
Step 4.4.1.1.1
Apply the distributive property.
Step 4.4.1.1.2
Multiply .
Step 4.4.1.1.2.1
Multiply by .
Step 4.4.1.1.2.2
Multiply by .
Step 4.4.1.2
To write as a fraction with a common denominator, multiply by .
Step 4.4.1.3
Combine and .
Step 4.4.1.4
Combine the numerators over the common denominator.
Step 4.4.1.5
Simplify the numerator.
Step 4.4.1.5.1
Multiply by .
Step 4.4.1.5.2
Subtract from .
Step 4.4.1.6
To write as a fraction with a common denominator, multiply by .
Step 4.4.1.7
Combine and .
Step 4.4.1.8
Combine the numerators over the common denominator.
Step 4.4.1.9
Combine the numerators over the common denominator.
Step 4.4.1.10
Multiply by .
Step 4.4.1.11
Subtract from .
Step 4.4.1.12
Factor out of .
Step 4.4.1.12.1
Factor out of .
Step 4.4.1.12.2
Factor out of .
Step 4.4.1.12.3
Factor out of .
Step 5
Step 5.1
Multiply both sides of the equation by .
Step 5.2
Simplify both sides of the equation.
Step 5.2.1
Simplify the left side.
Step 5.2.1.1
Simplify .
Step 5.2.1.1.1
Cancel the common factor of .
Step 5.2.1.1.1.1
Cancel the common factor.
Step 5.2.1.1.1.2
Rewrite the expression.
Step 5.2.1.1.2
Cancel the common factor of .
Step 5.2.1.1.2.1
Cancel the common factor.
Step 5.2.1.1.2.2
Rewrite the expression.
Step 5.2.2
Simplify the right side.
Step 5.2.2.1
Simplify .
Step 5.2.2.1.1
Cancel the common factor of .
Step 5.2.2.1.1.1
Factor out of .
Step 5.2.2.1.1.2
Cancel the common factor.
Step 5.2.2.1.1.3
Rewrite the expression.
Step 5.2.2.1.2
Multiply by .
Step 5.3
Move all terms not containing to the right side of the equation.
Step 5.3.1
Subtract from both sides of the equation.
Step 5.3.2
Subtract from .
Step 6
Step 6.1
Replace all occurrences of in with .
Step 6.2
Simplify the right side.
Step 6.2.1
Simplify .
Step 6.2.1.1
Simplify the numerator.
Step 6.2.1.1.1
Multiply by .
Step 6.2.1.1.2
Add and .
Step 6.2.1.2
Simplify the expression.
Step 6.2.1.2.1
Multiply by .
Step 6.2.1.2.2
Divide by .
Step 6.3
Replace all occurrences of in with .
Step 6.4
Simplify the right side.
Step 6.4.1
Simplify .
Step 6.4.1.1
Combine the numerators over the common denominator.
Step 6.4.1.2
Simplify the expression.
Step 6.4.1.2.1
Add and .
Step 6.4.1.2.2
Divide by .
Step 7
The solution to the system is the complete set of ordered pairs that are valid solutions.
Step 8
The result can be shown in multiple forms.
Point Form:
Equation Form: