Solve for a
a=-\frac{5-4x}{x-2}
x\neq 2
Solve for x
x=-\frac{5-2a}{a-4}
a\neq 4
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ax+5-2a=4x
Subtract 2a from both sides.
ax-2a=4x-5
Subtract 5 from both sides.
\left(x-2\right)a=4x-5
Combine all terms containing a.
\frac{\left(x-2\right)a}{x-2}=\frac{4x-5}{x-2}
Divide both sides by x-2.
a=\frac{4x-5}{x-2}
Dividing by x-2 undoes the multiplication by x-2.
ax+5-4x=2a
Subtract 4x from both sides.
ax-4x=2a-5
Subtract 5 from both sides.
\left(a-4\right)x=2a-5
Combine all terms containing x.
\frac{\left(a-4\right)x}{a-4}=\frac{2a-5}{a-4}
Divide both sides by a-4.
x=\frac{2a-5}{a-4}
Dividing by a-4 undoes the multiplication by a-4.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
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}