Which point is at distance ( \frac{11}{6} ) from ( \frac{3}{2} ) and lies to its left?

Correct answer: ( -\frac{1}{3} )

The direct answer is option B, \( -\frac{1}{3} \). On a number line, the distance between two points is the absolute difference of their coordinates. If a point must lie to the left of \(\frac{3}{2}\), we move left, so we subtract the distance: \(\frac{3}{2}-\frac{11}{6}\). Convert \(\frac{3}{2}\) to sixths: \(\frac{3}{2}=\frac{9}{6}\). Therefore \(\frac{9}{6}-\frac{11}{6}=-\frac{2}{6}=-\frac{1}{3}\). Checking confirms that \(\left| -\frac{1}{3}-\frac{3}{2}\right|=\left| -\frac{2}{6}-\frac{9}{6}\right|=\frac{11}{6}\), and \(-\frac{1}{3}\) is to the left. Option A, \(\frac{10}{3}\), is to the right and its distance is not \(\frac{11}{6}\). Option B is correct because it satisfies both distance and direction. Option C, \(\frac{1}{6}\), is also to the left, but its distance from \(\frac{3}{2}\) is \(\frac{4}{3}\), not \(\frac{11}{6}\). Option D, \(-\frac{11}{6}\), is to the left, but its distance is \(\frac{10}{3}\). Memory cue: left means subtract; right means add, and always check the absolute distance afterward.