Question

1. if uw = 6x - 35, find uw.

19 4x - 20
u v w

Explanation:

Step1: Set up equation

Since $UW = UV+VW$, we have $6x - 35=19+(4x - 20)$.

Step2: Simplify right - hand side

$19+(4x - 20)=4x+(19 - 20)=4x - 1$. So the equation becomes $6x - 35=4x - 1$.

Step3: Isolate x terms

Subtract $4x$ from both sides: $(6x - 4x)-35=(4x - 4x)-1$, which simplifies to $2x-35=-1$.

Step4: Isolate x

Add 35 to both sides: $2x-35 + 35=-1 + 35$, so $2x=34$. Then divide both sides by 2: $x = 17$.

Step5: Find UW

Substitute $x = 17$ into the expression for $UW$: $UW=6x - 35=6\times17-35=102 - 35=67$.

Answer:

67