Question

which value of x would make (overline{no}paralleloverline{kj})?
1
6
8
10

Explanation:

Step1: Apply the Basic Proportionality Theorem (Thales' Theorem)

If \( \overline{NO}\parallel\overline{KJ}\), then \(\frac{LN}{NK}=\frac{LO}{OJ}\).
Substitute \(LN = x - 3\), \(NK=x + 2\), \(LO=x - 4\), and \(OJ = x\) into the proportion: \(\frac{x-3}{x + 2}=\frac{x-4}{x}\).

Step2: Cross - multiply

Cross - multiplying gives \((x-3)x=(x - 4)(x + 2)\).
Expand both sides: \(x^{2}-3x=x^{2}+2x-4x-8\).

Step3: Simplify the equation

Simplify \(x^{2}-3x=x^{2}-2x - 8\).
Subtract \(x^{2}\) from both sides: \(-3x=-2x - 8\).
Add \(2x\) to both sides: \(-3x+2x=-8\), so \(-x=-8\).
Multiply both sides by \(- 1\): \(x = 8\).

Answer:

\(8\) (the third option)