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\frac{1}{2}\times 100+100x=150x
Use the distributive property to multiply \frac{1}{2}+x by 100.
\frac{100}{2}+100x=150x
Multiply \frac{1}{2} and 100 to get \frac{100}{2}.
50+100x=150x
Divide 100 by 2 to get 50.
50+100x-150x=0
Subtract 150x from both sides.
50-50x=0
Combine 100x and -150x to get -50x.
-50x=-50
Subtract 50 from both sides. Anything subtracted from zero gives its negation.
x=\frac{-50}{-50}
Divide both sides by -50.
x=1
Divide -50 by -50 to get 1.