Multiply each term by 25:
1<3-5x<15. Now split the inequality:
1<3-5x, 5x+1<3, 5x<2, x<⅖; or x<0.4
3-5x<15, 3-15<5x, -12<5x, -12/5<x, x>-12/5; or x>-2.4
So -2.4<x<0.4, that is, x can be anything between -2.4 and 0.4 (exclusively).
Since -2.4 is not included, if we substitute x=-2.4 in the original compound inequality we should fail to satisfy it:
(3-5x)/25=15/25=⅗, which just fails to satisfy the right-hand value.
Let's x=0.4: (3-5x)/25=1/25, which just fails to satisfy the left-hand value.
Now let's put x=0 and check (this should be OK to satisfy the inequality):
(3-5x)/25=3/25 which is between the limits 1/25 and 3/5.
ANSWER: -2.4<x<0.4