Solve for x
x = \frac{7}{2} = 3\frac{1}{2} = 3.5
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2\left(x-1\right)+x-2-3\left(x+1\right)=2\left(x-7\right)
Multiply both sides of the equation by 6, the least common multiple of 3,6,2.
2x-2+x-2-3\left(x+1\right)=2\left(x-7\right)
Use the distributive property to multiply 2 by x-1.
3x-2-2-3\left(x+1\right)=2\left(x-7\right)
Combine 2x and x to get 3x.
3x-4-3\left(x+1\right)=2\left(x-7\right)
Subtract 2 from -2 to get -4.
3x-4-3x-3=2\left(x-7\right)
Use the distributive property to multiply -3 by x+1.
-4-3=2\left(x-7\right)
Combine 3x and -3x to get 0.
-7=2\left(x-7\right)
Subtract 3 from -4 to get -7.
-7=2x-14
Use the distributive property to multiply 2 by x-7.
2x-14=-7
Swap sides so that all variable terms are on the left hand side.
2x=-7+14
Add 14 to both sides.
2x=7
Add -7 and 14 to get 7.
x=\frac{7}{2}
Divide both sides by 2.
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}