Basic Math Examples

Solve for c |(5c-4)/(3c-5)|=2
Step 1
Remove the absolute value term. This creates a on the right side of the equation because .
Step 2
The complete solution is the result of both the positive and negative portions of the solution.
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Step 2.1
First, use the positive value of the to find the first solution.
Step 2.2
Find the LCD of the terms in the equation.
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Step 2.2.1
Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.
Step 2.2.2
Remove parentheses.
Step 2.2.3
The LCM of one and any expression is the expression.
Step 2.3
Multiply each term in by to eliminate the fractions.
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Step 2.3.1
Multiply each term in by .
Step 2.3.2
Simplify the left side.
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Step 2.3.2.1
Cancel the common factor of .
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Step 2.3.2.1.1
Cancel the common factor.
Step 2.3.2.1.2
Rewrite the expression.
Step 2.3.3
Simplify the right side.
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Step 2.3.3.1
Apply the distributive property.
Step 2.3.3.2
Multiply.
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Step 2.3.3.2.1
Multiply by .
Step 2.3.3.2.2
Multiply by .
Step 2.4
Solve the equation.
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Step 2.4.1
Move all terms containing to the left side of the equation.
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Step 2.4.1.1
Subtract from both sides of the equation.
Step 2.4.1.2
Subtract from .
Step 2.4.2
Move all terms not containing to the right side of the equation.
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Step 2.4.2.1
Add to both sides of the equation.
Step 2.4.2.2
Add and .
Step 2.4.3
Divide each term in by and simplify.
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Step 2.4.3.1
Divide each term in by .
Step 2.4.3.2
Simplify the left side.
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Step 2.4.3.2.1
Dividing two negative values results in a positive value.
Step 2.4.3.2.2
Divide by .
Step 2.4.3.3
Simplify the right side.
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Step 2.4.3.3.1
Divide by .
Step 2.5
Next, use the negative value of the to find the second solution.
Step 2.6
Find the LCD of the terms in the equation.
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Step 2.6.1
Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.
Step 2.6.2
Remove parentheses.
Step 2.6.3
The LCM of one and any expression is the expression.
Step 2.7
Multiply each term in by to eliminate the fractions.
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Step 2.7.1
Multiply each term in by .
Step 2.7.2
Simplify the left side.
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Step 2.7.2.1
Cancel the common factor of .
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Step 2.7.2.1.1
Cancel the common factor.
Step 2.7.2.1.2
Rewrite the expression.
Step 2.7.3
Simplify the right side.
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Step 2.7.3.1
Apply the distributive property.
Step 2.7.3.2
Multiply.
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Step 2.7.3.2.1
Multiply by .
Step 2.7.3.2.2
Multiply by .
Step 2.8
Solve the equation.
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Step 2.8.1
Move all terms containing to the left side of the equation.
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Step 2.8.1.1
Add to both sides of the equation.
Step 2.8.1.2
Add and .
Step 2.8.2
Move all terms not containing to the right side of the equation.
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Step 2.8.2.1
Add to both sides of the equation.
Step 2.8.2.2
Add and .
Step 2.8.3
Divide each term in by and simplify.
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Step 2.8.3.1
Divide each term in by .
Step 2.8.3.2
Simplify the left side.
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Step 2.8.3.2.1
Cancel the common factor of .
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Step 2.8.3.2.1.1
Cancel the common factor.
Step 2.8.3.2.1.2
Divide by .
Step 2.9
The complete solution is the result of both the positive and negative portions of the solution.
Step 3
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
Mixed Number Form: