Solve for x (complex solution)
x\in \mathrm{C}
Solve for x
x\in \mathrm{R}
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\frac{1}{3}\times 9+\frac{1}{3}\left(-2\right)x-1=-\frac{2}{3}x+2
Use the distributive property to multiply \frac{1}{3} by 9-2x.
\frac{9}{3}+\frac{1}{3}\left(-2\right)x-1=-\frac{2}{3}x+2
Multiply \frac{1}{3} and 9 to get \frac{9}{3}.
3+\frac{1}{3}\left(-2\right)x-1=-\frac{2}{3}x+2
Divide 9 by 3 to get 3.
3+\frac{-2}{3}x-1=-\frac{2}{3}x+2
Multiply \frac{1}{3} and -2 to get \frac{-2}{3}.
3-\frac{2}{3}x-1=-\frac{2}{3}x+2
Fraction \frac{-2}{3} can be rewritten as -\frac{2}{3} by extracting the negative sign.
2-\frac{2}{3}x=-\frac{2}{3}x+2
Subtract 1 from 3 to get 2.
2-\frac{2}{3}x+\frac{2}{3}x=2
Add \frac{2}{3}x to both sides.
2=2
Combine -\frac{2}{3}x and \frac{2}{3}x to get 0.
\text{true}
Compare 2 and 2.
x\in \mathrm{C}
This is true for any x.
\frac{1}{3}\times 9+\frac{1}{3}\left(-2\right)x-1=-\frac{2}{3}x+2
Use the distributive property to multiply \frac{1}{3} by 9-2x.
\frac{9}{3}+\frac{1}{3}\left(-2\right)x-1=-\frac{2}{3}x+2
Multiply \frac{1}{3} and 9 to get \frac{9}{3}.
3+\frac{1}{3}\left(-2\right)x-1=-\frac{2}{3}x+2
Divide 9 by 3 to get 3.
3+\frac{-2}{3}x-1=-\frac{2}{3}x+2
Multiply \frac{1}{3} and -2 to get \frac{-2}{3}.
3-\frac{2}{3}x-1=-\frac{2}{3}x+2
Fraction \frac{-2}{3} can be rewritten as -\frac{2}{3} by extracting the negative sign.
2-\frac{2}{3}x=-\frac{2}{3}x+2
Subtract 1 from 3 to get 2.
2-\frac{2}{3}x+\frac{2}{3}x=2
Add \frac{2}{3}x to both sides.
2=2
Combine -\frac{2}{3}x and \frac{2}{3}x to get 0.
\text{true}
Compare 2 and 2.
x\in \mathrm{R}
This is true for any x.
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}