Algebra question? I5x-6I<0

Is the answer for this 6/5? or am I missing something?

yes, you're missing the simple definition of absolute value.
| a | ≥ 0 for all values of a, or of 5x - 6. since it can't be negative, there's no solution.

Let, |5x - 6| = y ;

y = - (5x - 6) ....................(1)

y = (5x - 6) .......................(2)

From (1),

x = - (y + 6)/5 .

From (2),

x = (y + 6)/5 .

since y < 0 , let y = - 1, then

x = - 1 and 1 ;

let y = - 2, then

x = - 4/5 and 4/5 ;

let y = - 6, then

x = 0.

Let, x = 7/5, then this value does not satisfy one of two equations namely (1) and (2).

Let, x = - 7/5, then this value does not satisfy either of those two equations.

Hence, - 6/5 < x < 6/5 .

No solution since absolute value of 5x - 6 can never be negative for any value of x. Let's take x = 0, then 5x - 6 = 5(0) - 6 = -6. Abs(-6) = 6 which is not less than zero. Try it with any value of x, that inequality will never be fulfilled.