Question

18 use the diagram to answer the question below.
if \\( \overline{rt} = 95 \\), solve for \\( x \\).
\\( x = \\) 16

Explanation:

Step1: Analyze the segment addition

The length of \( \overline{RT} \) is the sum of \( \overline{RS} \) and \( \overline{ST} \). So we have the equation \( (5x + 3) + (x + 8) = 95 \).

Step2: Combine like terms

Simplify the left side: \( 5x + x + 3 + 8 = 6x + 11 \). So the equation becomes \( 6x + 11 = 95 \).

Step3: Subtract 11 from both sides

\( 6x + 11 - 11 = 95 - 11 \), which simplifies to \( 6x = 84 \).

Step4: Divide both sides by 6

\( \frac{6x}{6} = \frac{84}{6} \), so \( x = 14 \).

Answer:

\( x = 14 \)