Solve for x
x=3
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\left(x-10\right)\times 2=\left(x-5\right)\times 7
Variable x cannot be equal to any of the values 5,10 since division by zero is not defined. Multiply both sides of the equation by \left(x-10\right)\left(x-5\right), the least common multiple of x-5,x-10.
2x-20=\left(x-5\right)\times 7
Use the distributive property to multiply x-10 by 2.
2x-20=7x-35
Use the distributive property to multiply x-5 by 7.
2x-20-7x=-35
Subtract 7x from both sides.
-5x-20=-35
Combine 2x and -7x to get -5x.
-5x=-35+20
Add 20 to both sides.
-5x=-15
Add -35 and 20 to get -15.
x=\frac{-15}{-5}
Divide both sides by -5.
x=3
Divide -15 by -5 to get 3.
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