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3x+2\left(2000-x\right)=5250
Multiply both sides of the equation by 150, the least common multiple of 50,75.
3x+4000-2x=5250
Use the distributive property to multiply 2 by 2000-x.
x+4000=5250
Combine 3x and -2x to get x.
x=5250-4000
Subtract 4000 from both sides.
x=1250
Subtract 4000 from 5250 to get 1250.