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100x=41\left(x+100\right)
Variable x cannot be equal to -100 since division by zero is not defined. Multiply both sides of the equation by 100\left(x+100\right), the least common multiple of 100+x,100.
100x=41x+4100
Use the distributive property to multiply 41 by x+100.
100x-41x=4100
Subtract 41x from both sides.
59x=4100
Combine 100x and -41x to get 59x.
x=\frac{4100}{59}
Divide both sides by 59.