Solve for x
x=-8
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\left(2x-4\right)\times 3-\left(2x+6\right)=\left(x-2\right)\times 5
Variable x cannot be equal to any of the values -3,2 since division by zero is not defined. Multiply both sides of the equation by 2\left(x-2\right)\left(x+3\right), the least common multiple of x+3,x-2,2x+6.
6x-12-\left(2x+6\right)=\left(x-2\right)\times 5
Use the distributive property to multiply 2x-4 by 3.
6x-12-2x-6=\left(x-2\right)\times 5
To find the opposite of 2x+6, find the opposite of each term.
4x-12-6=\left(x-2\right)\times 5
Combine 6x and -2x to get 4x.
4x-18=\left(x-2\right)\times 5
Subtract 6 from -12 to get -18.
4x-18=5x-10
Use the distributive property to multiply x-2 by 5.
4x-18-5x=-10
Subtract 5x from both sides.
-x-18=-10
Combine 4x and -5x to get -x.
-x=-10+18
Add 18 to both sides.
-x=8
Add -10 and 18 to get 8.
x=-8
Multiply both sides by -1.
Examples
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Linear equation
y = 3x + 4
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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}