Question

segment addition / subtraction (algebra)
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question
point v is on line segment \\(\overline{uw}\\). given \\(vw = x\\), \\(uv = 3x - 1\\), and \\(uw = 5x - 5\\), determine the numerical length of \\(vw\\).
answer attempt 1 out of 4
\\(vw = \square\\)
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Explanation:

Step1: Apply segment addition postulate

$UV + VW = UW$

Step2: Substitute given expressions

$(3x - 1) + x = 5x - 5$

Step3: Simplify left-hand side

$4x - 1 = 5x - 5$

Step4: Solve for $x$

$5 - 1 = 5x - 4x \implies x = 4$

Step5: Calculate length of $\overline{VW}$

$VW = x = 4$

Answer:

$4$