Question

if point e lies between point g and point o and ge = 2x + 3, eo = 3x - 8, and go = 45, find x.

Explanation:

Step1: Apply segment addition postulate

Since E is between G and O, \( GE + EO = GO \). Substitute the given expressions: \( (2x + 3) + (3x - 8) = 45 \).

Step2: Combine like terms

Simplify the left side: \( 2x + 3 + 3x - 8 = 5x - 5 \). So, \( 5x - 5 = 45 \).

Step3: Solve for x

Add 5 to both sides: \( 5x = 45 + 5 = 50 \). Divide by 5: \( x = \frac{50}{5} = 10 \).

Answer:

\( x = 10 \)