Solve for m (complex solution)
\left\{\begin{matrix}\\m=\frac{5}{2}=2.5\text{, }&\text{unconditionally}\\m\in \mathrm{C}\text{, }&x=5\end{matrix}\right.
Solve for x (complex solution)
\left\{\begin{matrix}\\x=5\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&m=\frac{5}{2}\end{matrix}\right.
Solve for m
\left\{\begin{matrix}\\m=\frac{5}{2}=2.5\text{, }&\text{unconditionally}\\m\in \mathrm{R}\text{, }&x=5\end{matrix}\right.
Solve for x
\left\{\begin{matrix}\\x=5\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&m=\frac{5}{2}\end{matrix}\right.
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2mx-5\left(x-1\right)=10m-20
Multiply both sides of the equation by 10, the least common multiple of 5,2.
2mx-5x+5=10m-20
Use the distributive property to multiply -5 by x-1.
2mx-5x+5-10m=-20
Subtract 10m from both sides.
2mx+5-10m=-20+5x
Add 5x to both sides.
2mx-10m=-20+5x-5
Subtract 5 from both sides.
2mx-10m=-25+5x
Subtract 5 from -20 to get -25.
\left(2x-10\right)m=-25+5x
Combine all terms containing m.
\left(2x-10\right)m=5x-25
The equation is in standard form.
\frac{\left(2x-10\right)m}{2x-10}=\frac{5x-25}{2x-10}
Divide both sides by 2x-10.
m=\frac{5x-25}{2x-10}
Dividing by 2x-10 undoes the multiplication by 2x-10.
m=\frac{5}{2}
Divide -25+5x by 2x-10.
2mx-5\left(x-1\right)=10m-20
Multiply both sides of the equation by 10, the least common multiple of 5,2.
2mx-5x+5=10m-20
Use the distributive property to multiply -5 by x-1.
2mx-5x=10m-20-5
Subtract 5 from both sides.
2mx-5x=10m-25
Subtract 5 from -20 to get -25.
\left(2m-5\right)x=10m-25
Combine all terms containing x.
\frac{\left(2m-5\right)x}{2m-5}=\frac{10m-25}{2m-5}
Divide both sides by -5+2m.
x=\frac{10m-25}{2m-5}
Dividing by -5+2m undoes the multiplication by -5+2m.
x=5
Divide 10m-25 by -5+2m.
2mx-5\left(x-1\right)=10m-20
Multiply both sides of the equation by 10, the least common multiple of 5,2.
2mx-5x+5=10m-20
Use the distributive property to multiply -5 by x-1.
2mx-5x+5-10m=-20
Subtract 10m from both sides.
2mx+5-10m=-20+5x
Add 5x to both sides.
2mx-10m=-20+5x-5
Subtract 5 from both sides.
2mx-10m=-25+5x
Subtract 5 from -20 to get -25.
\left(2x-10\right)m=-25+5x
Combine all terms containing m.
\left(2x-10\right)m=5x-25
The equation is in standard form.
\frac{\left(2x-10\right)m}{2x-10}=\frac{5x-25}{2x-10}
Divide both sides by 2x-10.
m=\frac{5x-25}{2x-10}
Dividing by 2x-10 undoes the multiplication by 2x-10.
m=\frac{5}{2}
Divide -25+5x by 2x-10.
2mx-5\left(x-1\right)=10m-20
Multiply both sides of the equation by 10, the least common multiple of 5,2.
2mx-5x+5=10m-20
Use the distributive property to multiply -5 by x-1.
2mx-5x=10m-20-5
Subtract 5 from both sides.
2mx-5x=10m-25
Subtract 5 from -20 to get -25.
\left(2m-5\right)x=10m-25
Combine all terms containing x.
\frac{\left(2m-5\right)x}{2m-5}=\frac{10m-25}{2m-5}
Divide both sides by -5+2m.
x=\frac{10m-25}{2m-5}
Dividing by -5+2m undoes the multiplication by -5+2m.
x=5
Divide 10m-25 by -5+2m.
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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
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