Algebra Examples

Solve for j 7/3-1/6j=1/6(2j-7)
Step 1
Combine and .
Step 2
Simplify .
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Step 2.1
Apply the distributive property.
Step 2.2
Cancel the common factor of .
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Step 2.2.1
Factor out of .
Step 2.2.2
Factor out of .
Step 2.2.3
Cancel the common factor.
Step 2.2.4
Rewrite the expression.
Step 2.3
Combine and .
Step 2.4
Combine and .
Step 2.5
Move the negative in front of the fraction.
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
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Step 3.3.1
Multiply by .
Step 3.3.2
Multiply by .
Step 3.4
Combine the numerators over the common denominator.
Step 3.5
Simplify each term.
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Step 3.5.1
Simplify the numerator.
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Step 3.5.1.1
Factor out of .
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Step 3.5.1.1.1
Factor out of .
Step 3.5.1.1.2
Factor out of .
Step 3.5.1.1.3
Factor out of .
Step 3.5.1.2
Multiply by .
Step 3.5.1.3
Subtract from .
Step 3.5.2
Cancel the common factor of and .
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Step 3.5.2.1
Factor out of .
Step 3.5.2.2
Cancel the common factors.
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Step 3.5.2.2.1
Factor out of .
Step 3.5.2.2.2
Cancel the common factor.
Step 3.5.2.2.3
Rewrite the expression.
Step 3.5.3
Move to the left of .
Step 3.5.4
Move the negative in front of the fraction.
Step 4
Move all terms not containing to the right side of the equation.
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Step 4.1
Subtract from both sides of the equation.
Step 4.2
To write as a fraction with a common denominator, multiply by .
Step 4.3
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Step 4.3.1
Multiply by .
Step 4.3.2
Multiply by .
Step 4.4
Combine the numerators over the common denominator.
Step 4.5
Simplify the numerator.
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Step 4.5.1
Multiply by .
Step 4.5.2
Subtract from .
Step 4.6
Cancel the common factor of and .
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Step 4.6.1
Factor out of .
Step 4.6.2
Cancel the common factors.
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Step 4.6.2.1
Factor out of .
Step 4.6.2.2
Cancel the common factor.
Step 4.6.2.3
Rewrite the expression.
Step 4.7
Move the negative in front of the fraction.
Step 5
Since the expression on each side of the equation has the same denominator, the numerators must be equal.
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
Dividing two negative values results in a positive value.
Step 6.2.2
Divide by .
Step 6.3
Simplify the right side.
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Step 6.3.1
Divide by .