Solve for a
a=3-\frac{5}{x}
x\neq 0
Solve for x
x=-\frac{5}{a-3}
a\neq 3
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ax=3x-5
Subtract 5 from both sides.
xa=3x-5
The equation is in standard form.
\frac{xa}{x}=\frac{3x-5}{x}
Divide both sides by x.
a=\frac{3x-5}{x}
Dividing by x undoes the multiplication by x.
a=3-\frac{5}{x}
Divide 3x-5 by x.
ax+5-3x=0
Subtract 3x from both sides.
ax-3x=-5
Subtract 5 from both sides. Anything subtracted from zero gives its negation.
\left(a-3\right)x=-5
Combine all terms containing x.
\frac{\left(a-3\right)x}{a-3}=-\frac{5}{a-3}
Divide both sides by a-3.
x=-\frac{5}{a-3}
Dividing by a-3 undoes the multiplication by a-3.
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}