Chemistry Examples

Find the Domain 6(y+7)gggggggg=3y
Step 1
Simplify .
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Step 1.1
Multiply by by adding the exponents.
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Step 1.1.1
Move .
Step 1.1.2
Multiply by .
Step 1.2
Multiply by by adding the exponents.
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Step 1.2.1
Move .
Step 1.2.2
Multiply by .
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Step 1.2.2.1
Raise to the power of .
Step 1.2.2.2
Use the power rule to combine exponents.
Step 1.2.3
Add and .
Step 1.3
Multiply by by adding the exponents.
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Step 1.3.1
Move .
Step 1.3.2
Multiply by .
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Step 1.3.2.1
Raise to the power of .
Step 1.3.2.2
Use the power rule to combine exponents.
Step 1.3.3
Add and .
Step 1.4
Multiply by by adding the exponents.
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Step 1.4.1
Move .
Step 1.4.2
Multiply by .
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Step 1.4.2.1
Raise to the power of .
Step 1.4.2.2
Use the power rule to combine exponents.
Step 1.4.3
Add and .
Step 1.5
Multiply by by adding the exponents.
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Step 1.5.1
Move .
Step 1.5.2
Multiply by .
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Step 1.5.2.1
Raise to the power of .
Step 1.5.2.2
Use the power rule to combine exponents.
Step 1.5.3
Add and .
Step 1.6
Multiply by by adding the exponents.
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Step 1.6.1
Move .
Step 1.6.2
Multiply by .
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Step 1.6.2.1
Raise to the power of .
Step 1.6.2.2
Use the power rule to combine exponents.
Step 1.6.3
Add and .
Step 1.7
Multiply by by adding the exponents.
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Step 1.7.1
Move .
Step 1.7.2
Multiply by .
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Step 1.7.2.1
Raise to the power of .
Step 1.7.2.2
Use the power rule to combine exponents.
Step 1.7.3
Add and .
Step 1.8
Apply the distributive property.
Step 1.9
Multiply by .
Step 1.10
Apply the distributive property.
Step 2
Subtract from both sides of the equation.
Step 3
Subtract from both sides of the equation.
Step 4
Factor out of .
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Step 4.1
Factor out of .
Step 4.2
Factor out of .
Step 4.3
Factor out of .
Step 5
Divide each term in by and simplify.
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Step 5.1
Divide each term in by .
Step 5.2
Simplify the left side.
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Step 5.2.1
Cancel the common factor of .
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Step 5.2.1.1
Cancel the common factor.
Step 5.2.1.2
Rewrite the expression.
Step 5.2.2
Cancel the common factor of .
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Step 5.2.2.1
Cancel the common factor.
Step 5.2.2.2
Divide by .
Step 5.3
Simplify the right side.
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Step 5.3.1
Cancel the common factor of and .
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Step 5.3.1.1
Factor out of .
Step 5.3.1.2
Cancel the common factors.
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Step 5.3.1.2.1
Cancel the common factor.
Step 5.3.1.2.2
Rewrite the expression.
Step 5.3.2
Move the negative in front of the fraction.
Step 6
Set the denominator in equal to to find where the expression is undefined.
Step 7
Solve for .
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Step 7.1
Add to both sides of the equation.
Step 7.2
Divide each term in by and simplify.
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Step 7.2.1
Divide each term in by .
Step 7.2.2
Simplify the left side.
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Step 7.2.2.1
Cancel the common factor of .
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Step 7.2.2.1.1
Cancel the common factor.
Step 7.2.2.1.2
Divide by .
Step 7.3
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 7.4
Simplify .
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Step 7.4.1
Rewrite as .
Step 7.4.2
Any root of is .
Step 7.5
The complete solution is the result of both the positive and negative portions of the solution.
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Step 7.5.1
First, use the positive value of the to find the first solution.
Step 7.5.2
Next, use the negative value of the to find the second solution.
Step 7.5.3
The complete solution is the result of both the positive and negative portions of the solution.
Step 8
The domain is all values of that make the expression defined.
Interval Notation:
Set-Builder Notation:
Step 9