Question

1. points e, h, and s are collinear with point h between points e and s. eh = 2x + 10 and hs = 6x - 2. a. what is the value of x when es = 80 b. what is eh? c. what is hs?

Explanation:

Part a:

Step1: Apply segment addition postulate

Since \( H \) is between \( E \) and \( S \), \( EH + HS = ES \). Substitute \( EH = 2x + 10 \), \( HS = 6x - 2 \), and \( ES = 80 \):
\( (2x + 10) + (6x - 2) = 80 \)

Step2: Simplify and solve for \( x \)

Combine like terms: \( 8x + 8 = 80 \)
Subtract 8 from both sides: \( 8x = 72 \)
Divide by 8: \( x = 9 \)

Step1: Substitute \( x = 9 \) into \( EH \) formula

\( EH = 2x + 10 \), substitute \( x = 9 \):
\( EH = 2(9) + 10 \)

Step2: Calculate \( EH \)

\( EH = 18 + 10 = 28 \)

Step1: Substitute \( x = 9 \) into \( HS \) formula

\( HS = 6x - 2 \), substitute \( x = 9 \):
\( HS = 6(9) - 2 \)

Step2: Calculate \( HS \)

\( HS = 54 - 2 = 52 \)

Answer:

\( x = 9 \)

Part b: