Question

wk, kr, and rp are shown, where wk = 2x - 2, kr = 3x, rp = x + 5, and wr = 18. diagram of w, k, r, p on a line find the value or length. x = dropdown wk = 6 dropdown kr = dropdown rp = dropdown wp = dropdown

Explanation:

Step1: Find x using WR = WK + KR

Given \( WK = 2x - 2 \), \( KR = 3x \), and \( WR = 18 \). So, \( WK + KR = WR \) gives \( (2x - 2) + 3x = 18 \).
Simplify: \( 5x - 2 = 18 \).
Add 2 to both sides: \( 5x = 20 \).
Divide by 5: \( x = 4 \).

Step2: Calculate KR

Substitute \( x = 4 \) into \( KR = 3x \): \( KR = 3(4) = 12 \).

Step3: Calculate RP

Substitute \( x = 4 \) into \( RP = x + 5 \): \( RP = 4 + 5 = 9 \).

Step4: Calculate WP

\( WP = WR + RP = 18 + 9 = 27 \). (Or \( WP = WK + KR + RP = 6 + 12 + 9 = 27 \))

Answer:

\( x = 4 \)
\( WK = 6 \) (given, verified as \( 2(4)-2=6 \))
\( KR = 12 \)
\( RP = 9 \)
\( WP = 27 \)