Question

if rs = 20, st = 17x, and rt = 19x + 14, what is rt?
diagram: line segment r---s---t with rs labeled 20, st labeled 17x, rt labeled 19x + 14
simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use segment addition postulate

From the number line, we know that \( RS + ST = RT \). Substituting the given values, we get \( 20 + 17x = 19x + 14 \).

Step2: Solve for \( x \)

Subtract \( 17x \) from both sides: \( 20 = 2x + 14 \). Then subtract 14 from both sides: \( 6 = 2x \). Divide both sides by 2: \( x = 3 \).

Step3: Find \( RT \)

Substitute \( x = 3 \) into the expression for \( RT \), which is \( 19x + 14 \). So \( RT = 19(3) + 14 = 57 + 14 = 71 \).

Answer:

71