Solve for x
x=32
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-75x=\frac{2}{75}\times \frac{200}{3}\times 75\left(x-50\right)
Variable x cannot be equal to 50 since division by zero is not defined. Multiply both sides of the equation by 75\left(x-50\right), the least common multiple of 50-x,75,3.
-75x=\frac{16}{9}\times 75\left(x-50\right)
Multiply \frac{2}{75} and \frac{200}{3} to get \frac{16}{9}.
-75x=\frac{400}{3}\left(x-50\right)
Multiply \frac{16}{9} and 75 to get \frac{400}{3}.
-75x=\frac{400}{3}x-\frac{20000}{3}
Use the distributive property to multiply \frac{400}{3} by x-50.
-75x-\frac{400}{3}x=-\frac{20000}{3}
Subtract \frac{400}{3}x from both sides.
-\frac{625}{3}x=-\frac{20000}{3}
Combine -75x and -\frac{400}{3}x to get -\frac{625}{3}x.
x=-\frac{20000}{3}\left(-\frac{3}{625}\right)
Multiply both sides by -\frac{3}{625}, the reciprocal of -\frac{625}{3}.
x=32
Multiply -\frac{20000}{3} and -\frac{3}{625} to get 32.
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