Question

The range of values of x which satisfy $\frac{-1}{3}\le \frac{x}{2}-\frac{4}{3}<\frac{1}{6}$, where x ϵ R is .

• A. $2\le x<3$
• B. $2<x<3$
• C. $3\le x<2$
• D. $2\le x\le 3$

Answer 1

The correct option is A $2\le x<3$

Given: $\frac{-1}{3}\le \frac{x}{2}-\frac{4}{3}<\frac{1}{6}$

$\frac{-1}{3}\le \frac{x}{2}-\frac{4}{3}$ and $\frac{x}{2}-\frac{4}{3}<\frac{1}{6}$, x $\in R$
Rule: If a term of an inequation is transferred from one side to the other side of the inequation, the sign of the term gets changed. Let's apply this rule in the following inequations.

$\frac{-1}{3}+\frac{4}{3}\le \frac{x}{2}$ and $\frac{x}{2}<\frac{1}{6}+\frac{4}{3}$, x $\in R$

1 $\le \frac{x}{2}$ and $\frac{x}{2}<\frac{3}{2}$

Rule: If both the sides of an inequation are multiplied or divided by the same positive number, then the sign of the inequality will remain the same.
On multiplying both sides by 2 in both the inequations;

$\Rightarrow$ 2 $\le$ x and $\Rightarrow$ x $<$ 3

Thus, 2 $\le$ x $<$ 3