Solve for E (complex solution)
\left\{\begin{matrix}E=-\frac{\left(1-x\right)\left(b+5\right)}{x}\text{, }&x\neq 0\\E\in \mathrm{C}\text{, }&b=-5\text{ and }x=0\end{matrix}\right.
Solve for b (complex solution)
\left\{\begin{matrix}b=-\frac{Ex-5x+5}{1-x}\text{, }&x\neq 1\\b\in \mathrm{C}\text{, }&x=1\text{ and }E=0\end{matrix}\right.
Solve for E
\left\{\begin{matrix}E=-\frac{\left(1-x\right)\left(b+5\right)}{x}\text{, }&x\neq 0\\E\in \mathrm{R}\text{, }&b=-5\text{ and }x=0\end{matrix}\right.
Solve for b
\left\{\begin{matrix}b=-\frac{Ex-5x+5}{1-x}\text{, }&x\neq 1\\b\in \mathrm{R}\text{, }&x=1\text{ and }E=0\end{matrix}\right.
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Ex+2-\left(bx-b\right)=5x-3
Use the distributive property to multiply b by x-1.
Ex+2-bx+b=5x-3
To find the opposite of bx-b, find the opposite of each term.
Ex-bx+b=5x-3-2
Subtract 2 from both sides.
Ex-bx+b=5x-5
Subtract 2 from -3 to get -5.
Ex+b=5x-5+bx
Add bx to both sides.
Ex=5x-5+bx-b
Subtract b from both sides.
xE=bx+5x-b-5
The equation is in standard form.
\frac{xE}{x}=\frac{\left(x-1\right)\left(b+5\right)}{x}
Divide both sides by x.
E=\frac{\left(x-1\right)\left(b+5\right)}{x}
Dividing by x undoes the multiplication by x.
Ex+2-\left(bx-b\right)=5x-3
Use the distributive property to multiply b by x-1.
Ex+2-bx+b=5x-3
To find the opposite of bx-b, find the opposite of each term.
2-bx+b=5x-3-Ex
Subtract Ex from both sides.
-bx+b=5x-3-Ex-2
Subtract 2 from both sides.
-bx+b=5x-5-Ex
Subtract 2 from -3 to get -5.
\left(-x+1\right)b=5x-5-Ex
Combine all terms containing b.
\left(1-x\right)b=-Ex+5x-5
The equation is in standard form.
\frac{\left(1-x\right)b}{1-x}=\frac{-Ex+5x-5}{1-x}
Divide both sides by -x+1.
b=\frac{-Ex+5x-5}{1-x}
Dividing by -x+1 undoes the multiplication by -x+1.
Ex+2-\left(bx-b\right)=5x-3
Use the distributive property to multiply b by x-1.
Ex+2-bx+b=5x-3
To find the opposite of bx-b, find the opposite of each term.
Ex-bx+b=5x-3-2
Subtract 2 from both sides.
Ex-bx+b=5x-5
Subtract 2 from -3 to get -5.
Ex+b=5x-5+bx
Add bx to both sides.
Ex=5x-5+bx-b
Subtract b from both sides.
xE=bx+5x-b-5
The equation is in standard form.
\frac{xE}{x}=\frac{\left(x-1\right)\left(b+5\right)}{x}
Divide both sides by x.
E=\frac{\left(x-1\right)\left(b+5\right)}{x}
Dividing by x undoes the multiplication by x.
Ex+2-\left(bx-b\right)=5x-3
Use the distributive property to multiply b by x-1.
Ex+2-bx+b=5x-3
To find the opposite of bx-b, find the opposite of each term.
2-bx+b=5x-3-Ex
Subtract Ex from both sides.
-bx+b=5x-3-Ex-2
Subtract 2 from both sides.
-bx+b=5x-5-Ex
Subtract 2 from -3 to get -5.
\left(-x+1\right)b=5x-5-Ex
Combine all terms containing b.
\left(1-x\right)b=-Ex+5x-5
The equation is in standard form.
\frac{\left(1-x\right)b}{1-x}=\frac{-Ex+5x-5}{1-x}
Divide both sides by 1-x.
b=\frac{-Ex+5x-5}{1-x}
Dividing by 1-x undoes the multiplication by 1-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}