Question

if uv = x + 1, vw = 2x, and uw = 10, what is uv? simplify your answer and write it as a proper fraction, mixed number, or

Explanation:

Step1: Set up the equation

From the number line, we know that \( UV + VW = UW \). Substituting the given expressions, we get \((x + 1)+2x = 10\).

Step2: Solve for \( x \)

Combine like terms: \( 3x + 1 = 10 \). Subtract 1 from both sides: \( 3x = 10 - 1 = 9 \). Then divide both sides by 3: \( x=\frac{9}{3}=3 \).

Step3: Find \( UV \)

Since \( UV = x + 1 \), substitute \( x = 3 \): \( UV = 3 + 1 = 4 \).

Answer:

\( 4 \)