Question

Find the solution set of the following inequalities and draw the graph of their solutions sets:
`|(x - 5)/(3)| < 6`

Answer 1

We have `|(x - 5)/(3)| < 6`
Using prop. | x | < a ⇒ - a < x < a
`|(x - 5)/(3)| < 6`
⇒ `-6< (x - 5)/(3) < 6`
⇒ -18< x -5 <18
⇒ 5 - 18< x <18 + 5
⇒ -13< x <23
So `|(x - 5)/(3)| < 6`
⇒ {x : - 13< x <23}
The graph of this set is