Solve for a
a=\frac{3w+7}{2}
Solve for w
w=\frac{2a-7}{3}
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6a-4a=3w+7
Subtract 4a from both sides.
2a=3w+7
Combine 6a and -4a to get 2a.
\frac{2a}{2}=\frac{3w+7}{2}
Divide both sides by 2.
a=\frac{3w+7}{2}
Dividing by 2 undoes the multiplication by 2.
3w+4a+7=6a
Swap sides so that all variable terms are on the left hand side.
3w+7=6a-4a
Subtract 4a from both sides.
3w+7=2a
Combine 6a and -4a to get 2a.
3w=2a-7
Subtract 7 from both sides.
\frac{3w}{3}=\frac{2a-7}{3}
Divide both sides by 3.
w=\frac{2a-7}{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
699 * 533
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}