Question

if rs = x + 7, st = 6, and rt = 4x - 14, what is rs? 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: $4x-14=(x + 7)+6$.

Step2: Simplify the right - hand side

$(x + 7)+6=x+7 + 6=x + 13$. So the equation becomes $4x-14=x + 13$.

Step3: Isolate the variable terms

Subtract $x$ from both sides: $4x-x-14=x-x + 13$, which simplifies to $3x-14=13$.

Step4: Isolate the $x$ term

Add 14 to both sides: $3x-14 + 14=13+14$, so $3x=27$.

Step5: Solve for $x$

Divide both sides by 3: $\frac{3x}{3}=\frac{27}{3}$, then $x = 9$.

Step6: Find the value of $RS$

Substitute $x = 9$ into the expression for $RS$. Since $RS=x + 7$, then $RS=9+7=16$.

Answer:

16