Question

if $uv = 12x$, $vw = 14x - 19$, and $uw = 20x - 7$, what is $uv$? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Apply segment addition postulate

From the diagram, \( UV + VW = UW \). Substitute the given expressions: \( 12x + (14x - 19) = 20x - 7 \).

Step2: Simplify left side

Combine like terms: \( 12x + 14x - 19 = 26x - 19 \). So equation is \( 26x - 19 = 20x - 7 \).

Step3: Solve for \( x \)

Subtract \( 20x \) from both sides: \( 26x - 20x - 19 = -7 \) → \( 6x - 19 = -7 \). Add 19 to both sides: \( 6x = -7 + 19 \) → \( 6x = 12 \). Divide by 6: \( x = \frac{12}{6} = 2 \).

Step4: Find \( UV \)

Substitute \( x = 2 \) into \( UV = 12x \): \( UV = 12 \times 2 = 24 \).

Answer:

24