A triangle has two sides of length 74 and 11.1 . What compound inequality describes the possible lengths for the third side, X? Write a compound inequality like 1lt xlt 3

## Step 1<br />The problem involves the use of the triangle inequality theorem, which states that the length of any side of a triangle must be less than the sum of the lengths of the other two sides and greater than the difference of the lengths of the other two sides.<br /><br />## Step 2<br />In this problem, the lengths of the two sides of the triangle are given as 74 and 11.1. Therefore, the possible lengths for the third side, denoted as X, must satisfy the following two inequalities:<br /><br />### \(74 - 11.1 < X < 74 + 11.1\)<br /><br />## Step 3<br />Solving the inequalities, we get:<br /><br />### \(62.9 < X < 85.1\)