Solve for x (complex solution)
x\in \mathrm{C}
Solve for x
x\in \mathrm{R}
Graph
Share
Copied to clipboard
12+2\left(x+1\right)-2\left(x-1\right)=2\left(-x+1\right)+12+2\left(x+1\right)
Multiply both sides of the equation by 4, the least common multiple of 2,4.
12+2x+2-2\left(x-1\right)=2\left(-x+1\right)+12+2\left(x+1\right)
Use the distributive property to multiply 2 by x+1.
14+2x-2\left(x-1\right)=2\left(-x+1\right)+12+2\left(x+1\right)
Add 12 and 2 to get 14.
14+2x-2x+2=2\left(-x+1\right)+12+2\left(x+1\right)
Use the distributive property to multiply -2 by x-1.
14+2=2\left(-x+1\right)+12+2\left(x+1\right)
Combine 2x and -2x to get 0.
16=2\left(-x+1\right)+12+2\left(x+1\right)
Add 14 and 2 to get 16.
16=2\left(-x\right)+2+12+2\left(x+1\right)
Use the distributive property to multiply 2 by -x+1.
16=2\left(-x\right)+14+2\left(x+1\right)
Add 2 and 12 to get 14.
16=2\left(-x\right)+14+2x+2
Use the distributive property to multiply 2 by x+1.
16=2\left(-x\right)+16+2x
Add 14 and 2 to get 16.
2\left(-x\right)+16+2x=16
Swap sides so that all variable terms are on the left hand side.
2\left(-x\right)+2x=16-16
Subtract 16 from both sides.
2\left(-x\right)+2x=0
Subtract 16 from 16 to get 0.
-2x+2x=0
Multiply 2 and -1 to get -2.
0=0
Combine -2x and 2x to get 0.
\text{true}
Compare 0 and 0.
x\in \mathrm{C}
This is true for any x.
12+2\left(x+1\right)-2\left(x-1\right)=2\left(-x+1\right)+12+2\left(x+1\right)
Multiply both sides of the equation by 4, the least common multiple of 2,4.
12+2x+2-2\left(x-1\right)=2\left(-x+1\right)+12+2\left(x+1\right)
Use the distributive property to multiply 2 by x+1.
14+2x-2\left(x-1\right)=2\left(-x+1\right)+12+2\left(x+1\right)
Add 12 and 2 to get 14.
14+2x-2x+2=2\left(-x+1\right)+12+2\left(x+1\right)
Use the distributive property to multiply -2 by x-1.
14+2=2\left(-x+1\right)+12+2\left(x+1\right)
Combine 2x and -2x to get 0.
16=2\left(-x+1\right)+12+2\left(x+1\right)
Add 14 and 2 to get 16.
16=2\left(-x\right)+2+12+2\left(x+1\right)
Use the distributive property to multiply 2 by -x+1.
16=2\left(-x\right)+14+2\left(x+1\right)
Add 2 and 12 to get 14.
16=2\left(-x\right)+14+2x+2
Use the distributive property to multiply 2 by x+1.
16=2\left(-x\right)+16+2x
Add 14 and 2 to get 16.
2\left(-x\right)+16+2x=16
Swap sides so that all variable terms are on the left hand side.
2\left(-x\right)+2x=16-16
Subtract 16 from both sides.
2\left(-x\right)+2x=0
Subtract 16 from 16 to get 0.
-2x+2x=0
Multiply 2 and -1 to get -2.
0=0
Combine -2x and 2x to get 0.
\text{true}
Compare 0 and 0.
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}