Question

if uv = x + 7, vw = 14, and uw = 3x + 1, 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 have the equation $3x + 1=(x + 7)+14$.

Step2: Simplify the right - hand side of the equation

$(x + 7)+14=x+21$, so the equation becomes $3x + 1=x + 21$.

Step3: Solve for x

Subtract x from both sides: $3x - x+1=x - x + 21$, which simplifies to $2x+1 = 21$. Then subtract 1 from both sides: $2x+1 - 1=21 - 1$, getting $2x=20$. Divide both sides by 2: $x=\frac{20}{2}=10$.

Step4: Find UV

Since $UV=x + 7$, substitute $x = 10$ into the expression for UV. So $UV=10 + 7=17$.

Answer:

17