Solve for Z
Z=\frac{a+i}{3}
Solve for a
a=3Z-i
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Z=\frac{a+i}{3}
Add 1 and 2 to get 3.
Z=\frac{1}{3}a+\frac{1}{3}i
Divide each term of a+i by 3 to get \frac{1}{3}a+\frac{1}{3}i.
Z=\frac{a+i}{3}
Add 1 and 2 to get 3.
Z=\frac{1}{3}a+\frac{1}{3}i
Divide each term of a+i by 3 to get \frac{1}{3}a+\frac{1}{3}i.
\frac{1}{3}a+\frac{1}{3}i=Z
Swap sides so that all variable terms are on the left hand side.
\frac{1}{3}a=Z-\frac{1}{3}i
Subtract \frac{1}{3}i from both sides.
\frac{\frac{1}{3}a}{\frac{1}{3}}=\frac{Z-\frac{1}{3}i}{\frac{1}{3}}
Multiply both sides by 3.
a=\frac{Z-\frac{1}{3}i}{\frac{1}{3}}
Dividing by \frac{1}{3} undoes the multiplication by \frac{1}{3}.
a=3Z-i
Divide Z-\frac{1}{3}i by \frac{1}{3} by multiplying Z-\frac{1}{3}i by the reciprocal of \frac{1}{3}.
Examples
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y = 3x + 4
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Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
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Limits
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