Finite Math Examples

Solve for z (3z)/5-(z-3)/2=(z+2)/3
Step 1
Multiply both sides by .
Step 2
Simplify.
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Step 2.1
Simplify the left side.
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Step 2.1.1
Simplify .
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Step 2.1.1.1
To write as a fraction with a common denominator, multiply by .
Step 2.1.1.2
To write as a fraction with a common denominator, multiply by .
Step 2.1.1.3
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Step 2.1.1.3.1
Multiply by .
Step 2.1.1.3.2
Multiply by .
Step 2.1.1.3.3
Multiply by .
Step 2.1.1.3.4
Multiply by .
Step 2.1.1.4
Combine the numerators over the common denominator.
Step 2.1.1.5
Simplify the numerator.
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Step 2.1.1.5.1
Multiply by .
Step 2.1.1.5.2
Apply the distributive property.
Step 2.1.1.5.3
Multiply by .
Step 2.1.1.5.4
Apply the distributive property.
Step 2.1.1.5.5
Multiply by .
Step 2.1.1.5.6
Multiply by .
Step 2.1.1.5.7
Subtract from .
Step 2.1.1.6
Combine fractions.
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Step 2.1.1.6.1
Combine and .
Step 2.1.1.6.2
Move to the left of .
Step 2.2
Simplify the right 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
Rewrite the expression.
Step 3
Solve for .
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Step 3.1
Multiply both sides by .
Step 3.2
Simplify.
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Step 3.2.1
Simplify the left side.
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Step 3.2.1.1
Simplify .
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Step 3.2.1.1.1
Cancel the common factor of .
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Step 3.2.1.1.1.1
Cancel the common factor.
Step 3.2.1.1.1.2
Rewrite the expression.
Step 3.2.1.1.2
Apply the distributive property.
Step 3.2.1.1.3
Multiply by .
Step 3.2.2
Simplify the right side.
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Step 3.2.2.1
Simplify .
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Step 3.2.2.1.1
Apply the distributive property.
Step 3.2.2.1.2
Simplify the expression.
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Step 3.2.2.1.2.1
Move to the left of .
Step 3.2.2.1.2.2
Multiply by .
Step 3.3
Solve for .
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Step 3.3.1
Move all terms containing to the left side of the equation.
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Step 3.3.1.1
Subtract from both sides of the equation.
Step 3.3.1.2
Subtract from .
Step 3.3.2
Move all terms not containing to the right side of the equation.
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Step 3.3.2.1
Subtract from both sides of the equation.
Step 3.3.2.2
Subtract from .
Step 3.3.3
Divide each term in by and simplify.
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Step 3.3.3.1
Divide each term in by .
Step 3.3.3.2
Simplify the left side.
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Step 3.3.3.2.1
Cancel the common factor of .
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Step 3.3.3.2.1.1
Cancel the common factor.
Step 3.3.3.2.1.2
Divide by .
Step 3.3.3.3
Simplify the right side.
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Step 3.3.3.3.1
Dividing two negative values results in a positive value.
Step 4
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
Mixed Number Form: