Question

if rs = 18, st = 5x + 4, and rt = 9x - 6, what is rt? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Set up equation based on segment - addition postulate

Since $RT=RS + ST$, we substitute the given expressions: $9x−6=18+(5x + 4)$.

Step2: Simplify the right - hand side of the equation

$9x−6=18 + 5x+4$, which simplifies to $9x−6=5x + 22$.

Step3: Isolate the variable terms

Subtract $5x$ from both sides: $9x-5x−6=5x-5x + 22$, resulting in $4x−6=22$.

Step4: Isolate the variable

Add 6 to both sides: $4x−6 + 6=22+6$, so $4x=28$.

Step5: Solve for x

Divide both sides by 4: $\frac{4x}{4}=\frac{28}{4}$, and $x = 7$.

Step6: Find the value of RT

Substitute $x = 7$ into the expression for $RT$: $RT=9x−6=9\times7−6$.
$RT=63−6=57$.

Answer:

57