Solve for x
x = \frac{9}{4} = 2\frac{1}{4} = 2.25
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6x+1+\left(x-5\right)\times 5=\left(x-2\right)\times 3
Variable x cannot be equal to any of the values 2,5 since division by zero is not defined. Multiply both sides of the equation by \left(x-5\right)\left(x-2\right), the least common multiple of x^{2}-7x+10,x-2,x-5.
6x+1+5x-25=\left(x-2\right)\times 3
Use the distributive property to multiply x-5 by 5.
11x+1-25=\left(x-2\right)\times 3
Combine 6x and 5x to get 11x.
11x-24=\left(x-2\right)\times 3
Subtract 25 from 1 to get -24.
11x-24=3x-6
Use the distributive property to multiply x-2 by 3.
11x-24-3x=-6
Subtract 3x from both sides.
8x-24=-6
Combine 11x and -3x to get 8x.
8x=-6+24
Add 24 to both sides.
8x=18
Add -6 and 24 to get 18.
x=\frac{18}{8}
Divide both sides by 8.
x=\frac{9}{4}
Reduce the fraction \frac{18}{8} to lowest terms by extracting and canceling out 2.
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Simultaneous equation
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\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
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Limits
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