Answer: x is greater than -1 and less than 9.
Explanation:
Let's solve the inequality step by step:
First, let's isolate the absolute value:
3*|x-4| - 5 < 10
=> 3*|x-4| < 10 + 5
=> 3*|x-4| < 15
Then, we divide both sides by 3 to get:
|x-4| < 15 / 3
=> |x-4| < 5
Now, remember that the definition of |a| < b is -b < a < b, so this becomes:
-5 < x-4 < 5
Next, we solve for x by adding 4 to all sides:
-5 + 4 < x < 5 + 4
So, the solution to the inequality is:
-1 < x < 9
Which means that x is greater than -1 and less than 9