Solve for x (complex solution)
x\in \mathrm{C}
Solve for x
x\in \mathrm{R}
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18\left(\frac{5}{3}x-\frac{1}{2}\right)-3=6\left(5x-2\right)
Multiply both sides of the equation by 30, the least common multiple of 5,3,2,10.
18\times \frac{5}{3}x+18\left(-\frac{1}{2}\right)-3=6\left(5x-2\right)
Use the distributive property to multiply 18 by \frac{5}{3}x-\frac{1}{2}.
\frac{18\times 5}{3}x+18\left(-\frac{1}{2}\right)-3=6\left(5x-2\right)
Express 18\times \frac{5}{3} as a single fraction.
\frac{90}{3}x+18\left(-\frac{1}{2}\right)-3=6\left(5x-2\right)
Multiply 18 and 5 to get 90.
30x+18\left(-\frac{1}{2}\right)-3=6\left(5x-2\right)
Divide 90 by 3 to get 30.
30x+\frac{18\left(-1\right)}{2}-3=6\left(5x-2\right)
Express 18\left(-\frac{1}{2}\right) as a single fraction.
30x+\frac{-18}{2}-3=6\left(5x-2\right)
Multiply 18 and -1 to get -18.
30x-9-3=6\left(5x-2\right)
Divide -18 by 2 to get -9.
30x-12=6\left(5x-2\right)
Subtract 3 from -9 to get -12.
30x-12=30x-12
Use the distributive property to multiply 6 by 5x-2.
30x-12-30x=-12
Subtract 30x from both sides.
-12=-12
Combine 30x and -30x to get 0.
\text{true}
Compare -12 and -12.
x\in \mathrm{C}
This is true for any x.
18\left(\frac{5}{3}x-\frac{1}{2}\right)-3=6\left(5x-2\right)
Multiply both sides of the equation by 30, the least common multiple of 5,3,2,10.
18\times \frac{5}{3}x+18\left(-\frac{1}{2}\right)-3=6\left(5x-2\right)
Use the distributive property to multiply 18 by \frac{5}{3}x-\frac{1}{2}.
\frac{18\times 5}{3}x+18\left(-\frac{1}{2}\right)-3=6\left(5x-2\right)
Express 18\times \frac{5}{3} as a single fraction.
\frac{90}{3}x+18\left(-\frac{1}{2}\right)-3=6\left(5x-2\right)
Multiply 18 and 5 to get 90.
30x+18\left(-\frac{1}{2}\right)-3=6\left(5x-2\right)
Divide 90 by 3 to get 30.
30x+\frac{18\left(-1\right)}{2}-3=6\left(5x-2\right)
Express 18\left(-\frac{1}{2}\right) as a single fraction.
30x+\frac{-18}{2}-3=6\left(5x-2\right)
Multiply 18 and -1 to get -18.
30x-9-3=6\left(5x-2\right)
Divide -18 by 2 to get -9.
30x-12=6\left(5x-2\right)
Subtract 3 from -9 to get -12.
30x-12=30x-12
Use the distributive property to multiply 6 by 5x-2.
30x-12-30x=-12
Subtract 30x from both sides.
-12=-12
Combine 30x and -30x to get 0.
\text{true}
Compare -12 and -12.
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}