Question

if $rs = 14$, $st = 7x + 2$, and $rt = 14x - 5$, what is $rt$? 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 \( RS + ST = RT \). Substituting the given values, we get \( 14+(7x + 2)=14x-5 \).

Step2: Simplify the left - hand side

Simplify \( 14+(7x + 2) \): \( 14 + 7x+2=7x + 16 \). So the equation becomes \( 7x+16 = 14x-5 \).

Step3: Solve for x

Subtract \( 7x \) from both sides: \( 16=14x - 7x-5 \), which simplifies to \( 16 = 7x-5 \). Then add 5 to both sides: \( 16 + 5=7x \), so \( 21 = 7x \). Divide both sides by 7: \( x=\frac{21}{7}=3 \).

Step4: Find the value of RT

We know that \( RT = 14x-5 \). Substitute \( x = 3 \) into the expression: \( RT=14\times3-5=42 - 5=37 \).

Answer:

\( 37 \)