Question

if st = x + 11, tu = 20, and su = 7x - 17, what is su?
diagram: line segment with points s, t, u; st labeled ( x + 11 ), tu labeled ( 20 ), su labeled ( 7x - 17 )
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 \( SU = ST + TU \). Substituting the given expressions, we get \( 7x - 17=(x + 11)+20 \).

Step2: Solve for x

Simplify the right - hand side: \( 7x - 17=x + 31 \).
Subtract \( x \) from both sides: \( 7x-x-17=x - x+ 31 \), which gives \( 6x-17 = 31 \).
Add 17 to both sides: \( 6x-17 + 17=31 + 17 \), so \( 6x=48 \).
Divide both sides by 6: \( x=\frac{48}{6}=8 \).

Step3: Find the length of SU

Substitute \( x = 8 \) into the expression for \( SU \), which is \( 7x-17 \).
\( SU=7\times8-17=56 - 17 = 39 \).

Answer:

39