Solve for x
x = \frac{20}{7} = 2\frac{6}{7} \approx 2.857142857
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\frac{5}{2}=\frac{x}{4-x}
Divide 5 by 5 to get 1.
\frac{x}{4-x}=\frac{5}{2}
Swap sides so that all variable terms are on the left hand side.
-2x=5\left(x-4\right)
Variable x cannot be equal to 4 since division by zero is not defined. Multiply both sides of the equation by 2\left(x-4\right), the least common multiple of 4-x,2.
-2x=5x-20
Use the distributive property to multiply 5 by x-4.
-2x-5x=-20
Subtract 5x from both sides.
-7x=-20
Combine -2x and -5x to get -7x.
x=\frac{-20}{-7}
Divide both sides by -7.
x=\frac{20}{7}
Fraction \frac{-20}{-7} can be simplified to \frac{20}{7} by removing the negative sign from both the numerator and the denominator.
Examples
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{ 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}