Finite Math Examples

Find the Inverse 25x+15y=975
Step 1
Subtract from both sides of the equation.
Step 2
Divide each term in by and simplify.
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Step 2.1
Divide each term in by .
Step 2.2
Simplify the left side.
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Step 2.2.1
Cancel the common factor of .
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Step 2.2.1.1
Cancel the common factor.
Step 2.2.1.2
Divide by .
Step 2.3
Simplify the right side.
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Step 2.3.1
Simplify each term.
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Step 2.3.1.1
Divide by .
Step 2.3.1.2
Cancel the common factor of and .
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Step 2.3.1.2.1
Factor out of .
Step 2.3.1.2.2
Cancel the common factors.
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Step 2.3.1.2.2.1
Factor out of .
Step 2.3.1.2.2.2
Cancel the common factor.
Step 2.3.1.2.2.3
Rewrite the expression.
Step 2.3.1.3
Move the negative in front of the fraction.
Step 3
Interchange the variables.
Step 4
Solve for .
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Step 4.1
Rewrite the equation as .
Step 4.2
Subtract from both sides of the equation.
Step 4.3
Multiply both sides of the equation by .
Step 4.4
Simplify both sides of the equation.
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Step 4.4.1
Simplify the left side.
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Step 4.4.1.1
Simplify .
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Step 4.4.1.1.1
Cancel the common factor of .
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Step 4.4.1.1.1.1
Move the leading negative in into the numerator.
Step 4.4.1.1.1.2
Move the leading negative in into the numerator.
Step 4.4.1.1.1.3
Factor out of .
Step 4.4.1.1.1.4
Cancel the common factor.
Step 4.4.1.1.1.5
Rewrite the expression.
Step 4.4.1.1.2
Cancel the common factor of .
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Step 4.4.1.1.2.1
Factor out of .
Step 4.4.1.1.2.2
Cancel the common factor.
Step 4.4.1.1.2.3
Rewrite the expression.
Step 4.4.1.1.3
Multiply.
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Step 4.4.1.1.3.1
Multiply by .
Step 4.4.1.1.3.2
Multiply by .
Step 4.4.2
Simplify the right side.
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Step 4.4.2.1
Simplify .
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Step 4.4.2.1.1
Simplify terms.
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Step 4.4.2.1.1.1
Apply the distributive property.
Step 4.4.2.1.1.2
Combine and .
Step 4.4.2.1.1.3
Cancel the common factor of .
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Step 4.4.2.1.1.3.1
Move the leading negative in into the numerator.
Step 4.4.2.1.1.3.2
Factor out of .
Step 4.4.2.1.1.3.3
Cancel the common factor.
Step 4.4.2.1.1.3.4
Rewrite the expression.
Step 4.4.2.1.1.4
Multiply by .
Step 4.4.2.1.2
Move to the left of .
Step 5
Replace with to show the final answer.
Step 6
Verify if is the inverse of .
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Step 6.1
To verify the inverse, check if and .
Step 6.2
Evaluate .
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Step 6.2.1
Set up the composite result function.
Step 6.2.2
Evaluate by substituting in the value of into .
Step 6.2.3
Simplify each term.
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Step 6.2.3.1
Cancel the common factor of and .
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Step 6.2.3.1.1
Factor out of .
Step 6.2.3.1.2
Cancel the common factors.
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Step 6.2.3.1.2.1
Factor out of .
Step 6.2.3.1.2.2
Cancel the common factor.
Step 6.2.3.1.2.3
Rewrite the expression.
Step 6.2.3.1.2.4
Divide by .
Step 6.2.3.2
Apply the distributive property.
Step 6.2.3.3
Multiply by .
Step 6.2.3.4
Cancel the common factor of .
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Step 6.2.3.4.1
Move the leading negative in into the numerator.
Step 6.2.3.4.2
Cancel the common factor.
Step 6.2.3.4.3
Rewrite the expression.
Step 6.2.3.5
Apply the distributive property.
Step 6.2.3.6
Multiply by .
Step 6.2.3.7
Multiply .
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Step 6.2.3.7.1
Multiply by .
Step 6.2.3.7.2
Multiply by .
Step 6.2.4
Combine the opposite terms in .
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Step 6.2.4.1
Add and .
Step 6.2.4.2
Add and .
Step 6.3
Evaluate .
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Step 6.3.1
Set up the composite result function.
Step 6.3.2
Evaluate by substituting in the value of into .
Step 6.3.3
Simplify each term.
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Step 6.3.3.1
Cancel the common factor of and .
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Step 6.3.3.1.1
Factor out of .
Step 6.3.3.1.2
Cancel the common factors.
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Step 6.3.3.1.2.1
Factor out of .
Step 6.3.3.1.2.2
Cancel the common factor.
Step 6.3.3.1.2.3
Rewrite the expression.
Step 6.3.3.1.2.4
Divide by .
Step 6.3.3.2
Apply the distributive property.
Step 6.3.3.3
Cancel the common factor of .
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Step 6.3.3.3.1
Move the leading negative in into the numerator.
Step 6.3.3.3.2
Cancel the common factor.
Step 6.3.3.3.3
Rewrite the expression.
Step 6.3.3.4
Multiply by .
Step 6.3.3.5
Apply the distributive property.
Step 6.3.3.6
Multiply .
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Step 6.3.3.6.1
Multiply by .
Step 6.3.3.6.2
Multiply by .
Step 6.3.3.7
Multiply by .
Step 6.3.4
Combine the opposite terms in .
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Step 6.3.4.1
Subtract from .
Step 6.3.4.2
Add and .
Step 6.4
Since and , then is the inverse of .