Solve for x
x = \frac{9}{5} = 1\frac{4}{5} = 1.8
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2\left(5-\frac{x-2}{2}\right)=3\left(3x-2\right)
Multiply both sides of the equation by 6, the least common multiple of 3,2.
10+2\left(-\frac{x-2}{2}\right)=3\left(3x-2\right)
Use the distributive property to multiply 2 by 5-\frac{x-2}{2}.
10+\frac{-2\left(x-2\right)}{2}=3\left(3x-2\right)
Express 2\left(-\frac{x-2}{2}\right) as a single fraction.
10-\left(x-2\right)=3\left(3x-2\right)
Cancel out 2 and 2.
10-x-\left(-2\right)=3\left(3x-2\right)
To find the opposite of x-2, find the opposite of each term.
10-x+2=3\left(3x-2\right)
The opposite of -2 is 2.
12-x=3\left(3x-2\right)
Add 10 and 2 to get 12.
12-x=9x-6
Use the distributive property to multiply 3 by 3x-2.
12-x-9x=-6
Subtract 9x from both sides.
12-10x=-6
Combine -x and -9x to get -10x.
-10x=-6-12
Subtract 12 from both sides.
-10x=-18
Subtract 12 from -6 to get -18.
x=\frac{-18}{-10}
Divide both sides by -10.
x=\frac{9}{5}
Reduce the fraction \frac{-18}{-10} to lowest terms by extracting and canceling out -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}