Question

Find the range of values of x which satisfy $\frac{-1}{3}\le \frac{x}{2}-\frac{4}{3}<\frac{1}{6}$, where x ϵ real number.

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

Answer 1

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

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

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 the inequation by 6, we get;

$\frac{-1}{3}\le \frac{3x-8}{6}<\frac{1}{6}$

$\Rightarrow -2\le (3x-8)<1$

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 given inequation.

$\Rightarrow -2+8\le 3x<1+8$

$\Rightarrow 6\le 3x<9$

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 dividing the inequation by 2, we get;

$\Rightarrow 2\le x<3$