Solve for k (complex solution)
\left\{\begin{matrix}\\k=\frac{1}{2}=0.5\text{, }&\text{unconditionally}\\k\in \mathrm{C}\text{, }&x=2\end{matrix}\right.
Solve for x (complex solution)
\left\{\begin{matrix}\\x=2\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&k=\frac{1}{2}\end{matrix}\right.
Solve for k
\left\{\begin{matrix}\\k=\frac{1}{2}=0.5\text{, }&\text{unconditionally}\\k\in \mathrm{R}\text{, }&x=2\end{matrix}\right.
Solve for x
\left\{\begin{matrix}\\x=2\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&k=\frac{1}{2}\end{matrix}\right.
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2kx-4k=x-2
Use the distributive property to multiply 2k by x-2.
\left(2x-4\right)k=x-2
Combine all terms containing k.
\frac{\left(2x-4\right)k}{2x-4}=\frac{x-2}{2x-4}
Divide both sides by 2x-4.
k=\frac{x-2}{2x-4}
Dividing by 2x-4 undoes the multiplication by 2x-4.
k=\frac{1}{2}
Divide -2+x by 2x-4.
2kx-4k=x-2
Use the distributive property to multiply 2k by x-2.
2kx-4k-x=-2
Subtract x from both sides.
2kx-x=-2+4k
Add 4k to both sides.
\left(2k-1\right)x=-2+4k
Combine all terms containing x.
\left(2k-1\right)x=4k-2
The equation is in standard form.
\frac{\left(2k-1\right)x}{2k-1}=\frac{4k-2}{2k-1}
Divide both sides by -1+2k.
x=\frac{4k-2}{2k-1}
Dividing by -1+2k undoes the multiplication by -1+2k.
x=2
Divide -2+4k by -1+2k.
2kx-4k=x-2
Use the distributive property to multiply 2k by x-2.
\left(2x-4\right)k=x-2
Combine all terms containing k.
\frac{\left(2x-4\right)k}{2x-4}=\frac{x-2}{2x-4}
Divide both sides by 2x-4.
k=\frac{x-2}{2x-4}
Dividing by 2x-4 undoes the multiplication by 2x-4.
k=\frac{1}{2}
Divide -2+x by 2x-4.
2kx-4k=x-2
Use the distributive property to multiply 2k by x-2.
2kx-4k-x=-2
Subtract x from both sides.
2kx-x=-2+4k
Add 4k to both sides.
\left(2k-1\right)x=-2+4k
Combine all terms containing x.
\left(2k-1\right)x=4k-2
The equation is in standard form.
\frac{\left(2k-1\right)x}{2k-1}=\frac{4k-2}{2k-1}
Divide both sides by -1+2k.
x=\frac{4k-2}{2k-1}
Dividing by -1+2k undoes the multiplication by -1+2k.
x=2
Divide -2+4k by -1+2k.
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}