Question

1. find x
2. find \\(\overline{xy}\\)
3. find \\(\overline{xz}\\)

(diagram: line segment xyz with ( xy = 9x + 2 ), ( yz = 5 ), ( xz = 14x - 8 ))

Explanation:

1) Find \( x \)

Step 1: Analyze the segment relationships

From the diagram, we know that \( XY + YZ = XZ \). So \( 9x + 2 + 5 = 14x - 8 \).

Step 2: Simplify the equation

Simplify the left - hand side: \( 9x+7 = 14x - 8 \).

Step 3: Solve for \( x \)

Subtract \( 9x \) from both sides: \( 7=14x - 9x-8 \), which simplifies to \( 7 = 5x-8 \).
Add 8 to both sides: \( 7 + 8=5x \), so \( 15 = 5x \).
Divide both sides by 5: \( x=\frac{15}{5}=3 \).

Step 1: Substitute \( x = 3 \) into the expression for \( XY \)

The expression for \( XY \) is \( 9x + 2 \). Substitute \( x = 3 \): \( 9\times3+2 \).

Step 2: Calculate the value

\( 9\times3 = 27 \), then \( 27+2=29 \).

Step 1: Substitute \( x = 3 \) into the expression for \( XZ \)

The expression for \( XZ \) is \( 14x - 8 \). Substitute \( x = 3 \): \( 14\times3-8 \).

Step 2: Calculate the value

\( 14\times3=42 \), then \( 42 - 8 = 34 \).
Or we can also use \( XY+YZ \) to calculate \( XZ \). Since \( XY = 29 \) and \( YZ = 5 \), \( XZ=29 + 5=34 \).

Answer:

\( x = 3 \)

2) Find \( \overline{XY} \)