Question

What is x 5/18-x-2/9<x-4/6

Answer 1

$\dfrac{5}{18}-x-\dfrac{2}{9} < x-\dfrac{4}{6}\qquad|\cdot36\\\\36\cdot\dfrac{5}{18}-36x-36\cdot\dfrac{2}{9} < 36x-36\cdot\dfrac{4}{6}\\\\2\cdot5-36x-4\cdot2 < 36x-6\cdot4\\\\10-36x-8 < 36x-24\\\\(10-8)-36x < 36x-24\\\\2-36x < 36x-24\qquad|-2\\\\-36x < 36x-26\qquad|-36x\\\\-72x < -26\qquad|\text{change the signs}\\\\72x > 26\qquad|:72\\\\x > \dfrac{26}{72}\\\\x > \dfrac{13}{36}$