Question

if tu = x + 3, uv = 5x, and tv = 9, what is uv? diagram: line segment t to v with u between them; tu labeled ( x + 3 ), uv labeled ( 5x ), tv labeled 9 simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Set up the equation

From the number line, we know that \( TU + UV = TV \). Substituting the given expressions, we get \((x + 3)+5x = 9\).

Step2: Combine like terms

Simplify the left - hand side of the equation: \(x+5x + 3=9\), which becomes \(6x+3 = 9\).

Step3: Solve for x

Subtract 3 from both sides: \(6x=9 - 3\), so \(6x = 6\). Then divide both sides by 6: \(x=\frac{6}{6}=1\).

Step4: Find the value of UV

We know that \(UV = 5x\). Substitute \(x = 1\) into the expression for \(UV\): \(UV=5\times1 = 5\).

Answer:

5