Solve for x
x = \frac{13}{5} = 2\frac{3}{5} = 2.6
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-2\left(x-2\right)=3\left(x-3\right)
Variable x cannot be equal to 3 since division by zero is not defined. Multiply both sides of the equation by 2\left(x-3\right), the least common multiple of 3-x,2.
-2x+4=3\left(x-3\right)
Use the distributive property to multiply -2 by x-2.
-2x+4=3x-9
Use the distributive property to multiply 3 by x-3.
-2x+4-3x=-9
Subtract 3x from both sides.
-5x+4=-9
Combine -2x and -3x to get -5x.
-5x=-9-4
Subtract 4 from both sides.
-5x=-13
Subtract 4 from -9 to get -13.
x=\frac{-13}{-5}
Divide both sides by -5.
x=\frac{13}{5}
Fraction \frac{-13}{-5} can be simplified to \frac{13}{5} by removing the negative sign from both the numerator and the denominator.
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}