Question

if rs = 16x - 12, st = 6x - 6, and rt = 20x + 14, what is rt? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use segment - addition postulate

Since $RT=RS + ST$, we substitute the given expressions: $(16x - 12)+(6x - 6)=20x + 14$.

Step2: Combine like - terms on the left - hand side

$16x+6x-12 - 6=20x + 14$, which simplifies to $22x-18 = 20x + 14$.

Step3: Isolate the variable $x$

Subtract $20x$ from both sides: $22x-20x-18=20x-20x + 14$, getting $2x-18 = 14$. Then add 18 to both sides: $2x-18 + 18=14 + 18$, so $2x=32$.

Step4: Solve for $x$

Divide both sides by 2: $\frac{2x}{2}=\frac{32}{2}$, so $x = 16$.

Step5: Find the value of $RT$

Substitute $x = 16$ into the expression for $RT$: $RT=20x + 14=20\times16+14$.
$RT=320 + 14=334$.

Answer:

$334$