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 variable terms

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

Step4: Isolate the variable

Add 35 to both sides: $2x-35 + 35=-1 + 35$, getting $2x=34$.

Step5: Solve for x

Divide both sides by 2: $\frac{2x}{2}=\frac{34}{2}$, so $x = 17$.

Step6: Find UW

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

Answer:

67