Q.Assertion (A) : Solution set of inequality $|3x - 2| \leq \dfrac{1}{2}$, $x \in R$ is $\left[\dfrac{1}{2}, \dfrac{5}{6}\right]$. Reason (R) : $|x - a| \leq r \Leftrightarrow x \leq a - r$ or $x \geq a + r$. (A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A). (B) Both Assertion (A) and Reason (R) are true, but Reason (R) is $not$ the correct explanation of the Assertion (A). (C) Assertion (A) is true, but Reason (R) is false. (D) Assertion (A) is false, but Reason (R) is true.

An inequality compares two expressions using $<$, $\le$, $>$ or $\ge$, and its solution is a range of values rather than a single number.

A linear inequality in one variable (e.g. $3x - 5 < 7$) is solved just like a linear equation, with one crucial rule: multiplying or dividing both sides by a negative number reverses the inequality sign. The answer is an interval such as $x < 4$, i.e. $(-\infty, 4)$. When the variable is restricted to a domain — natural numbers $\mathbb{N}$, whole numbers, or integers $\mathbb{Z}$ — only the values of that type lying inside the range are solutions. …