Find the range of possible measures of the third side. Use the variable \( x \). \[ 22,18 \]

To find the range of possible measures for the third side \( x \) of a triangle with sides measuring 22 and 18, you can use the triangle inequality theorem. This theorem states that the sum of any two sides must be greater than the third side. 1. From \( 22 + 18 > x \), we get \( x < 40 \). 2. From \( 22 + x > 18 \), we deduce \( x > -4 \) (which isn't useful since side lengths can't be negative). 3. From \( 18 + x > 22 \), we find \( x > 4 \). Putting it all together, the third side \( x \) must satisfy \( 4 < x < 40 \). Thus, the range of possible measures for the third side is \( (4, 40) \).