Question

if (uv = 7x - 13), (vw=x + 4), and (uw = 15), what is (uv)? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use segment - addition postulate

Since $UW = UV+VW$, we substitute the given expressions: $15=(7x - 13)+(x + 4)$.

Step2: Simplify the right - hand side

Combine like terms: $15 = 7x-13+x + 4$, which simplifies to $15=8x-9$.

Step3: Solve for x

Add 9 to both sides of the equation: $15 + 9=8x-9 + 9$, so $24 = 8x$. Then divide both sides by 8: $x=\frac{24}{8}=3$.

Step4: Find UV

Substitute $x = 3$ into the expression for $UV$: $UV=7x-13=7\times3-13$.
Calculate $7\times3-13=21 - 13 = 8$.

Answer:

8