Question

which value of x would make \\(\overline{lk} \parallel \overline{om}\\)?
\\(\bigcirc\\) \\(x = 2\\)
\\(\bigcirc\\) \\(x = 2.4\\)
\\(\bigcirc\\) \\(x = 4.8\\)
\\(\bigcirc\\) \\(x = 8\\)
(image shows a geometric figure with points n, k, m on a line segment, and l, o with segments labeled x, x+2, x-3, x-4)

Explanation:

Step1: Apply Basic Proportionality Theorem

If $\overline{LK} \parallel \overline{OM}$, then $\frac{NK}{NM} = \frac{NL}{NO}$. Here, $NK = x+2$, $NM = (x+2)+(x-3) = 2x-1$, $NL = x$, $NO = x+(x-4) = 2x-4$. So:
$$\frac{x+2}{2x-1} = \frac{x}{2x-4}$$

Step2: Cross-multiply to solve for x

$$(x+2)(2x-4) = x(2x-1)$$
Expand both sides:
Left: $2x^2 -4x +4x -8 = 2x^2 -8$
Right: $2x^2 -x$

Set equal:
$$2x^2 -8 = 2x^2 -x$$

Cancel $2x^2$:
$$-8 = -x \implies x=8$$

Answer:

D. x = 8