Solve for a 1/9a-1/18+1/3a=1/3+a

Math
19a-118+13a=13+a
Simplify 19a-118+13a.
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Simplify each term.
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Combine 19 and a.
a9-118+13a=13+a
Combine 13 and a.
a9-118+a3=13+a
a9-118+a3=13+a
To write a3 as a fraction with a common denominator, multiply by 33.
a9+a3⋅33-118=13+a
Write each expression with a common denominator of 9, by multiplying each by an appropriate factor of 1.
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Multiply a3 and 33.
a9+a⋅33⋅3-118=13+a
Multiply 3 by 3.
a9+a⋅39-118=13+a
a9+a⋅39-118=13+a
Combine the numerators over the common denominator.
a+a⋅39-118=13+a
Add a and a⋅3.
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Reorder a and 3.
a+3⋅a9-118=13+a
Add a and 3⋅a.
4a9-118=13+a
4a9-118=13+a
4a9-118=13+a
Move all terms containing a to the left side of the equation.
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Subtract a from both sides of the equation.
4a9-118-a=13
To write -a as a fraction with a common denominator, multiply by 99.
4a9-a⋅99-118=13
Combine -a and 99.
4a9+-a⋅99-118=13
Combine the numerators over the common denominator.
4a-a⋅99-118=13
Simplify each term.
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Simplify the numerator.
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Factor a out of 4a-a⋅9.
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Factor a out of 4a.
a⋅4-a⋅99-118=13
Factor a out of -a⋅9.
a⋅4+a(-1⋅9)9-118=13
Factor a out of a⋅4+a(-1⋅9).
a(4-1⋅9)9-118=13
a(4-1⋅9)9-118=13
Multiply -1 by 9.
a(4-9)9-118=13
Subtract 9 from 4.
a⋅-59-118=13
a⋅-59-118=13
Move -5 to the left of a.
-5⋅a9-118=13
Move the negative in front of the fraction.
-5a9-118=13
-5a9-118=13
-5a9-118=13
Move all terms not containing a to the right side of the equation.
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Add 118 to both sides of the equation.
-5a9=13+118
To write 13 as a fraction with a common denominator, multiply by 66.
-5a9=13⋅66+118
Write each expression with a common denominator of 18, by multiplying each by an appropriate factor of 1.
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Multiply 13 and 66.
-5a9=63⋅6+118
Multiply 3 by 6.
-5a9=618+118
-5a9=618+118
Combine the numerators over the common denominator.
-5a9=6+118
Add 6 and 1.
-5a9=718
-5a9=718
Multiply both sides of the equation by -95.
-95⋅(-5a9)=-95⋅718
Simplify both sides of the equation.
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Simplify -95⋅(-5a9).
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Cancel the common factor of 9.
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Move the leading negative in -95 into the numerator.
-95⋅(-5a9)=-95⋅718
Move the leading negative in -5a9 into the numerator.
-95⋅-5a9=-95⋅718
Factor 9 out of -9.
9(-1)5⋅-5a9=-95⋅718
Cancel the common factor.
9⋅-15⋅-5a9=-95⋅718
Rewrite the expression.
-15⋅(-5a)=-95⋅718
-15⋅(-5a)=-95⋅718
Cancel the common factor of 5.
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Factor 5 out of -5a.
-15⋅(5(-a))=-95⋅718
Cancel the common factor.
-15⋅(5(-a))=-95⋅718
Rewrite the expression.
-1⋅(-a)=-95⋅718
-1⋅(-a)=-95⋅718
Multiply.
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Multiply -1 by -1.
1⋅a=-95⋅718
Multiply a by 1.
a=-95⋅718
a=-95⋅718
a=-95⋅718
Simplify -95⋅718.
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Cancel the common factor of 9.
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Move the leading negative in -95 into the numerator.
a=-95⋅718
Factor 9 out of -9.
a=9(-1)5⋅718
Factor 9 out of 18.
a=9⋅-15⋅79⋅2
Cancel the common factor.
a=9⋅-15⋅79⋅2
Rewrite the expression.
a=-15⋅72
a=-15⋅72
Multiply -15 and 72.
a=-1⋅75⋅2
Simplify the expression.
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Multiply -1 by 7.
a=-75⋅2
Multiply 5 by 2.
a=-710
Move the negative in front of the fraction.
a=-710
a=-710
a=-710
a=-710
The result can be shown in multiple forms.
Exact Form:
a=-710
Decimal Form:
a=-0.7
Solve for a 1/9a-1/18+1/3a=1/3+a

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