Pre-Algebra Examples

Solve for y (2y)/3=1/2*(-3/2+y/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
Cancel the common factor of .
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Step 2.1.1.1
Cancel the common factor.
Step 2.1.1.2
Rewrite the expression.
Step 2.2
Simplify the right side.
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Step 2.2.1
Simplify .
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Step 2.2.1.1
Apply the distributive property.
Step 2.2.1.2
Multiply .
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Step 2.2.1.2.1
Multiply by .
Step 2.2.1.2.2
Multiply by .
Step 2.2.1.3
Multiply .
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Step 2.2.1.3.1
Multiply by .
Step 2.2.1.3.2
Multiply by .
Step 2.2.1.4
Apply the distributive property.
Step 2.2.1.5
Multiply .
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Step 2.2.1.5.1
Multiply by .
Step 2.2.1.5.2
Combine and .
Step 2.2.1.5.3
Multiply by .
Step 2.2.1.6
Cancel the common factor of .
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Step 2.2.1.6.1
Factor out of .
Step 2.2.1.6.2
Cancel the common factor.
Step 2.2.1.6.3
Rewrite the expression.
Step 2.2.1.7
Simplify the expression.
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Step 2.2.1.7.1
Move the negative in front of the fraction.
Step 2.2.1.7.2
Reorder and .
Step 3
Solve for .
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Step 3.1
Move all terms containing to the left side of the equation.
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Step 3.1.1
Subtract from both sides of the equation.
Step 3.1.2
To write as a fraction with a common denominator, multiply by .
Step 3.1.3
Combine and .
Step 3.1.4
Combine the numerators over the common denominator.
Step 3.1.5
Simplify the numerator.
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Step 3.1.5.1
Factor out of .
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Step 3.1.5.1.1
Factor out of .
Step 3.1.5.1.2
Factor out of .
Step 3.1.5.1.3
Factor out of .
Step 3.1.5.2
Multiply by .
Step 3.1.5.3
Subtract from .
Step 3.1.6
Move to the left of .
Step 3.2
Multiply both sides of the equation by .
Step 3.3
Simplify both sides of the equation.
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Step 3.3.1
Simplify the left side.
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Step 3.3.1.1
Simplify .
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Step 3.3.1.1.1
Cancel the common factor of .
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Step 3.3.1.1.1.1
Cancel the common factor.
Step 3.3.1.1.1.2
Rewrite the expression.
Step 3.3.1.1.2
Cancel the common factor of .
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Step 3.3.1.1.2.1
Factor out of .
Step 3.3.1.1.2.2
Cancel the common factor.
Step 3.3.1.1.2.3
Rewrite the expression.
Step 3.3.2
Simplify the right side.
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Step 3.3.2.1
Simplify .
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Step 3.3.2.1.1
Cancel the common factor of .
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Step 3.3.2.1.1.1
Move the leading negative in into the numerator.
Step 3.3.2.1.1.2
Factor out of .
Step 3.3.2.1.1.3
Cancel the common factor.
Step 3.3.2.1.1.4
Rewrite the expression.
Step 3.3.2.1.2
Cancel the common factor of .
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Step 3.3.2.1.2.1
Factor out of .
Step 3.3.2.1.2.2
Cancel the common factor.
Step 3.3.2.1.2.3
Rewrite the expression.
Step 3.3.2.1.3
Move the negative in front of the fraction.
Step 4
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
Mixed Number Form: