Question

if $rs = 2x$, $st = x + 1$, and $rt = 4$, what is $rs$?
simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Set up the equation

From the line segment, we know that \( RS + ST = RT \). Substituting the given expressions, we get \( 2x+(x + 1)=4 \).

Step2: Solve for x

Simplify the left - hand side of the equation: \( 2x+x + 1=4 \), which combines like terms to \( 3x+1 = 4 \).
Subtract 1 from both sides: \( 3x=4 - 1=3 \).
Divide both sides by 3: \( x = 1 \).

Step3: Find RS

Since \( RS = 2x \) and \( x = 1 \), then \( RS=2\times1 = 2 \).

Answer:

2