Question

what is the range of possible sizes for side x?

Explanation:

Step1: Apply triangle inequality theorem (difference)

The difference of two sides of a triangle is less than the third side. So \(|6.0 - 5.8|\lt x\).
\(6.0−5.8 = 0.2\), so \(0.2\lt x\).

Step2: Apply triangle inequality theorem (sum)

The sum of two sides of a triangle is greater than the third side. So \(x\lt6.0 + 5.8\).
\(6.0+5.8=11.8\), so \(x\lt11.8\).

Answer:

\(0.2\lt x\lt11.8\)