Basic Math Examples

Solve for q (q-3)/2-(4q-7)/5=2 1/2
Step 1
Simplify the left side.
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Step 1.1
Simplify .
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Step 1.1.1
To write as a fraction with a common denominator, multiply by .
Step 1.1.2
To write as a fraction with a common denominator, multiply by .
Step 1.1.3
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Step 1.1.3.1
Multiply by .
Step 1.1.3.2
Multiply by .
Step 1.1.3.3
Multiply by .
Step 1.1.3.4
Multiply by .
Step 1.1.4
Combine the numerators over the common denominator.
Step 1.1.5
Simplify the numerator.
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Step 1.1.5.1
Apply the distributive property.
Step 1.1.5.2
Move to the left of .
Step 1.1.5.3
Multiply by .
Step 1.1.5.4
Apply the distributive property.
Step 1.1.5.5
Multiply by .
Step 1.1.5.6
Multiply by .
Step 1.1.5.7
Apply the distributive property.
Step 1.1.5.8
Multiply by .
Step 1.1.5.9
Multiply by .
Step 1.1.5.10
Subtract from .
Step 1.1.5.11
Add and .
Step 1.1.6
Simplify with factoring out.
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Step 1.1.6.1
Factor out of .
Step 1.1.6.2
Rewrite as .
Step 1.1.6.3
Factor out of .
Step 1.1.6.4
Simplify the expression.
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Step 1.1.6.4.1
Rewrite as .
Step 1.1.6.4.2
Move the negative in front of the fraction.
Step 2
Simplify the right side.
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Step 2.1
Convert to an improper fraction.
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Step 2.1.1
A mixed number is an addition of its whole and fractional parts.
Step 2.1.2
Add and .
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Step 2.1.2.1
To write as a fraction with a common denominator, multiply by .
Step 2.1.2.2
Combine and .
Step 2.1.2.3
Combine the numerators over the common denominator.
Step 2.1.2.4
Simplify the numerator.
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Step 2.1.2.4.1
Multiply by .
Step 2.1.2.4.2
Add and .
Step 3
Multiply both sides of the equation by .
Step 4
Simplify both sides of the equation.
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Step 4.1
Simplify the left side.
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Step 4.1.1
Simplify .
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Step 4.1.1.1
Cancel the common factor of .
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Step 4.1.1.1.1
Move the leading negative in into the numerator.
Step 4.1.1.1.2
Factor out of .
Step 4.1.1.1.3
Cancel the common factor.
Step 4.1.1.1.4
Rewrite the expression.
Step 4.1.1.2
Multiply.
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Step 4.1.1.2.1
Multiply by .
Step 4.1.1.2.2
Multiply by .
Step 4.2
Simplify the right side.
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Step 4.2.1
Simplify .
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Step 4.2.1.1
Cancel the common factor of .
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Step 4.2.1.1.1
Factor out of .
Step 4.2.1.1.2
Cancel the common factor.
Step 4.2.1.1.3
Rewrite the expression.
Step 4.2.1.2
Multiply by .
Step 5
Move all terms not containing to the right side of the equation.
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Step 5.1
Subtract from both sides of the equation.
Step 5.2
Subtract from .
Step 6
Divide each term in by and simplify.
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Step 6.1
Divide each term in by .
Step 6.2
Simplify the left side.
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Step 6.2.1
Cancel the common factor of .
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Step 6.2.1.1
Cancel the common factor.
Step 6.2.1.2
Divide by .
Step 6.3
Simplify the right side.
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Step 6.3.1
Move the negative in front of the fraction.
Step 7
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
Mixed Number Form: