Book: Calculus with analytic geometry ( fourth edition )by protter and protter.

Problems(page 6 )

x/3-x < 2

= x< 2(3-x) by distribution

= x < 6-2x by adding 2x both side

= 3x < 6 by dividing 3 both side

x < 2 answer

please check my work if i done correctly. I'm little confuse when can i use cases in inequalities. Thank you in advance