Finite Math Examples

Solve for x y=(2425.01(1-(1+0.11)^(-(12-x))))/(0.11/2)
Step 1
Rewrite the equation as .
Step 2
Multiply both sides by .
Step 3
Simplify.
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Step 3.1
Simplify the left side.
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Step 3.1.1
Simplify .
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Step 3.1.1.1
Combine fractions.
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Step 3.1.1.1.1
Combine.
Step 3.1.1.1.2
Multiply by .
Step 3.1.1.1.3
Combine and .
Step 3.1.1.1.4
Multiply by .
Step 3.1.1.2
Simplify the numerator.
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Step 3.1.1.2.1
Add and .
Step 3.1.1.2.2
Apply the distributive property.
Step 3.1.1.2.3
Multiply by .
Step 3.1.1.2.4
Multiply .
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Step 3.1.1.2.4.1
Multiply by .
Step 3.1.1.2.4.2
Multiply by .
Step 3.1.1.3
Simplify with factoring out.
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Step 3.1.1.3.1
Divide by .
Step 3.1.1.3.2
Factor out of .
Step 3.1.1.4
Separate fractions.
Step 3.1.1.5
Simplify the expression.
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Step 3.1.1.5.1
Divide by .
Step 3.1.1.5.2
Divide by .
Step 3.1.1.6
Apply the distributive property.
Step 3.1.1.7
Simplify the expression.
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Step 3.1.1.7.1
Multiply by .
Step 3.1.1.7.2
Multiply by .
Step 3.1.1.7.3
Reorder and .
Step 3.2
Simplify the right side.
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Step 3.2.1
Simplify .
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Step 3.2.1.1
Divide by .
Step 3.2.1.2
Move to the left of .
Step 4
Solve for .
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Step 4.1
Subtract from both sides of the equation.
Step 4.2
Divide each term in by and simplify.
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Step 4.2.1
Divide each term in by .
Step 4.2.2
Simplify the left side.
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Step 4.2.2.1
Cancel the common factor of .
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Step 4.2.2.1.1
Cancel the common factor.
Step 4.2.2.1.2
Divide by .
Step 4.2.3
Simplify the right side.
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Step 4.2.3.1
Simplify each term.
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Step 4.2.3.1.1
Move the negative in front of the fraction.
Step 4.2.3.1.2
Factor out of .
Step 4.2.3.1.3
Factor out of .
Step 4.2.3.1.4
Separate fractions.
Step 4.2.3.1.5
Divide by .
Step 4.2.3.1.6
Divide by .
Step 4.2.3.1.7
Multiply by .
Step 4.2.3.1.8
Divide by .
Step 4.3
Take the natural logarithm of both sides of the equation to remove the variable from the exponent.
Step 4.4
Expand by moving outside the logarithm.
Step 4.5
Simplify the left side.
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Step 4.5.1
Apply the distributive property.
Step 4.6
Move all the terms containing a logarithm to the left side of the equation.
Step 4.7
Move all terms not containing to the right side of the equation.
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Step 4.7.1
Add to both sides of the equation.
Step 4.7.2
Add to both sides of the equation.
Step 4.8
Divide each term in by and simplify.
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Step 4.8.1
Divide each term in by .
Step 4.8.2
Simplify the left side.
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Step 4.8.2.1
Cancel the common factor of .
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Step 4.8.2.1.1
Cancel the common factor.
Step 4.8.2.1.2
Divide by .
Step 4.8.3
Simplify the right side.
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Step 4.8.3.1
Cancel the common factor of .
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Step 4.8.3.1.1
Cancel the common factor.
Step 4.8.3.1.2
Divide by .