Facing Problem in defining regions in modulous with 3 variable

The issue is that you’re not splitting using all the critical points together. In modulus, regions are formed where the sign inside each expression stays the same, so you must take all breakpoints: here x = 1, 3, 5.

So the correct regions are:

x < 1

1 ≤ x < 3

3 ≤ x < 5

x ≥ 5

Not just <3 and <5. In each region, remove modulus based on the sign and solve.

Just remember: regions come from where each bracket becomes zero.