Solve for W
W=3d-r
Solve for d
d=\frac{r+W}{3}
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3d-W=r
Swap sides so that all variable terms are on the left hand side.
-W=r-3d
Subtract 3d from both sides.
\frac{-W}{-1}=\frac{r-3d}{-1}
Divide both sides by -1.
W=\frac{r-3d}{-1}
Dividing by -1 undoes the multiplication by -1.
W=-\left(r-3d\right)
Divide r-3d by -1.
3d-W=r
Swap sides so that all variable terms are on the left hand side.
3d=r+W
Add W to both sides.
\frac{3d}{3}=\frac{r+W}{3}
Divide both sides by 3.
d=\frac{r+W}{3}
Dividing by 3 undoes the multiplication by 3.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
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Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
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
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}