How do you solve the following inequality 1 divided by l6x-5l is less than or equal to 5. 6x-5 is in absolute value.?

Split it into two cases.

First - 6x-5 is positive(greater or equal to zero):

Equation will get following form:

6x-5 <= 5

This resolves to x <= 10/6.

Second case - 6x-5 is less than zero:

Equation will get following form:

-6x+5 <= 5

This resolves to x >= 0.

As we can see, x has to be both greater than zero and less than or equal to 10/6, and this is our answer.

0 <= x <= 10/6