solve x-4<1/8 write solution using set builder notation

To solve the inequality x - 4 < 1/8, we need to isolate the variable x.

Step 1: Add 4 to both sides of the inequality to get rid of the -4 on the left side:
x - 4 + 4 < 1/8 + 4/1
x < 1/8 + 32/8
x < (1 + 32)/8
x < 33/8

The solution to the inequality is x < 33/8.

Now, let's express this solution using set-builder notation.

Set-builder notation uses braces { } to indicate a set, and a vertical bar | to separate the element and the condition. So, the set-builder notation for x < 33/8 would be:

{x | x is a real number and x is less than 33/8}