Question

point v is on line segment uw. given vw = 5x - 4, uv = 2x, and uw = 5x, determine the numerical length of vw. answer attempt 1 out of 2

Explanation:

Step1: Use segment - addition postulate

Since $UV + VW=UW$, we substitute the given expressions: $2x+(5x - 4)=5x$.

Step2: Simplify the left - hand side

Combine like terms: $2x+5x - 4=7x - 4$. So, $7x - 4 = 5x$.

Step3: Solve for $x$

Subtract $5x$ from both sides: $7x-5x - 4=5x - 5x$, which gives $2x-4 = 0$. Then add 4 to both sides: $2x-4 + 4=0 + 4$, so $2x=4$. Divide both sides by 2: $x = 2$.

Step4: Find the length of $VW$

Substitute $x = 2$ into the expression for $VW$. $VW=5x - 4$. Then $VW=5\times2-4=10 - 4=6$.

Answer:

6