Basic Math Examples

Solve for a (3a-5)/12+(a+4)/2=(5a-7)/14+a/2
Step 1
Simplify .
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Step 1.1
To write as a fraction with a common denominator, multiply by .
Step 1.2
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Step 1.2.1
Multiply by .
Step 1.2.2
Multiply by .
Step 1.3
Combine the numerators over the common denominator.
Step 1.4
Simplify the numerator.
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Step 1.4.1
Apply the distributive property.
Step 1.4.2
Move to the left of .
Step 1.4.3
Multiply by .
Step 1.4.4
Add and .
Step 1.4.5
Add and .
Step 2
Simplify .
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Step 2.1
To write as a fraction with a common denominator, multiply by .
Step 2.2
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Step 2.2.1
Multiply by .
Step 2.2.2
Multiply by .
Step 2.3
Combine the numerators over the common denominator.
Step 2.4
Simplify the numerator.
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Step 2.4.1
Move to the left of .
Step 2.4.2
Add and .
Step 3
Move all terms containing to the left side of the equation.
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Step 3.1
Subtract from both sides of the equation.
Step 3.2
To write as a fraction with a common denominator, multiply by .
Step 3.3
To write as a fraction with a common denominator, multiply by .
Step 3.4
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Step 3.4.1
Multiply by .
Step 3.4.2
Multiply by .
Step 3.4.3
Multiply by .
Step 3.4.4
Multiply by .
Step 3.5
Combine the numerators over the common denominator.
Step 3.6
Simplify the numerator.
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Step 3.6.1
Apply the distributive property.
Step 3.6.2
Multiply by .
Step 3.6.3
Multiply by .
Step 3.6.4
Apply the distributive property.
Step 3.6.5
Multiply by .
Step 3.6.6
Multiply by .
Step 3.6.7
Apply the distributive property.
Step 3.6.8
Multiply by .
Step 3.6.9
Multiply by .
Step 3.6.10
Subtract from .
Step 3.6.11
Add and .
Step 3.7
Factor out of .
Step 3.8
Rewrite as .
Step 3.9
Factor out of .
Step 3.10
Rewrite as .
Step 3.11
Move the negative in front of the fraction.
Step 4
Set the numerator equal to zero.
Step 5
Solve the equation for .
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Step 5.1
Add to both sides of the equation.
Step 5.2
Divide each term in by and simplify.
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Step 5.2.1
Divide each term in by .
Step 5.2.2
Simplify the left side.
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Step 5.2.2.1
Cancel the common factor of .
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Step 5.2.2.1.1
Cancel the common factor.
Step 5.2.2.1.2
Divide by .
Step 6
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
Mixed Number Form: