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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
Remove parentheses.
Step 2.2.1.2
Simplify each term.
Step 2.2.1.2.1
Apply the distributive property.
Step 2.2.1.2.2
Simplify.
Step 2.2.1.2.2.1
Multiply by .
Step 2.2.1.2.2.2
Multiply by .
Step 2.2.1.2.2.3
Multiply by .
Step 2.2.1.3
Simplify by adding terms.
Step 2.2.1.3.1
Add and .
Step 2.2.1.3.2
Add and .
Step 2.3
Replace all occurrences of in with .
Step 2.4
Simplify the left side.
Step 2.4.1
Simplify .
Step 2.4.1.1
Simplify each term.
Step 2.4.1.1.1
Apply the distributive property.
Step 2.4.1.1.2
Simplify.
Step 2.4.1.1.2.1
Multiply by .
Step 2.4.1.1.2.2
Multiply by .
Step 2.4.1.1.2.3
Multiply by .
Step 2.4.1.2
Simplify by adding terms.
Step 2.4.1.2.1
Add and .
Step 2.4.1.2.2
Add and .
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
Subtract from both sides of the equation.
Step 3.1.3
Subtract from .
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
Factor out of .
Step 3.2.3.1.2
Factor out of .
Step 3.2.3.1.3
Separate fractions.
Step 3.2.3.1.4
Divide by .
Step 3.2.3.1.5
Divide by .
Step 3.2.3.1.6
Divide by .
Step 4
Step 4.1
Replace all occurrences of in with .
Step 4.2
Simplify .
Step 4.2.1
Simplify the left side.
Step 4.2.1.1
Simplify .
Step 4.2.1.1.1
Simplify each term.
Step 4.2.1.1.1.1
Apply the distributive property.
Step 4.2.1.1.1.2
Multiply by .
Step 4.2.1.1.1.3
Multiply by .
Step 4.2.1.1.2
Simplify by adding terms.
Step 4.2.1.1.2.1
Add and .
Step 4.2.1.1.2.2
Subtract from .
Step 4.2.2
Simplify the right side.
Step 4.2.2.1
Simplify .
Step 4.2.2.1.1
Simplify each term.
Step 4.2.2.1.1.1
Apply the distributive property.
Step 4.2.2.1.1.2
Multiply by .
Step 4.2.2.1.1.3
Multiply by .
Step 4.2.2.1.2
Simplify by adding terms.
Step 4.2.2.1.2.1
Add and .
Step 4.2.2.1.2.2
Subtract from .
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 by .
Step 4.4.1.1.3
Multiply by .
Step 4.4.1.2
Simplify by adding terms.
Step 4.4.1.2.1
Add and .
Step 4.4.1.2.2
Subtract from .
Step 5
Step 5.1
Move all terms containing to the left side of the equation.
Step 5.1.1
Add to both sides of the equation.
Step 5.1.2
Add and .
Step 5.2
Move all terms not containing to the right side of the equation.
Step 5.2.1
Subtract from both sides of the equation.
Step 5.2.2
Subtract from .
Step 5.3
Divide each term in by and simplify.
Step 5.3.1
Divide each term in by .
Step 5.3.2
Simplify the left side.
Step 5.3.2.1
Cancel the common factor of .
Step 5.3.2.1.1
Cancel the common factor.
Step 5.3.2.1.2
Divide by .
Step 5.3.3
Simplify the right side.
Step 5.3.3.1
Divide by .
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
Multiply by .
Step 6.2.1.2
Add and .
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
Multiply by .
Step 6.4.1.2
Subtract from .
Step 7
The solution to the system is the complete set of ordered pairs that are valid solutions.