Question

if uv = 2x - 6, vw = 14, and uw = 5x - 16, what is uw? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Set up equation

Since $UW=UV + VW$, we have $5x-16=(2x - 6)+14$.

Step2: Simplify right - hand side

$(2x - 6)+14=2x+( - 6 + 14)=2x + 8$. So the equation becomes $5x-16=2x + 8$.

Step3: Isolate x terms

Subtract $2x$ from both sides: $5x-2x-16=2x-2x + 8$, which simplifies to $3x-16=8$.

Step4: Isolate x

Add 16 to both sides: $3x-16 + 16=8 + 16$, so $3x=24$.

Step5: Solve for x

Divide both sides by 3: $x=\frac{24}{3}=8$.

Step6: Find UW

Substitute $x = 8$ into the expression for $UW$: $UW=5x-16=5\times8-16=40 - 16=24$.

Answer:

24