-x + 11 < 4x - 4 < 9x - 29

This inequality is actually a compound inequality, which means it's two inequalities in one. We can solve it by breaking it down into two separate inequalities and solving each one individually.

First, let's solve the left inequality: -x + 11 < 4x - 4.

Step 1: Add x to both sides to get rid of the negative x on the left side. This gives us 11 < 5x - 4.

Step 2: Add 4 to both sides to isolate the term with x on the right side. This gives us 15 < 5x.

Step 3: Divide both sides by 5 to solve for x. This gives us x > 3.

Now, let's solve the right inequality: 4x - 4 < 9x - 29.

Step 1: Subtract 4x from both sides to get -4 < 5x - 29.

Step 2: Add 29 to both sides to isolate the term with x on the right side. This gives us 25 < 5x.

Step 3: Divide both sides by 5 to solve for x. This gives us x > 5.

So, the solution to the compound inequality -x + 11 < 4x - 4 < 9x - 29 is x > 3 and x > 5. Since x has to satisfy both inequalities, the final solution is x > 5.