Which of the following number line represents the solution of the inequation:
$2 + 4 x < 2 x - 5 \leq 3 x; x \in Z$ .

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None of these

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Solution

The correct option is B

Given: $2 + 4 x < 2 x - 5 \leq 3 x$

Let's separate the inequation in two inequations.

$2 + 4 x < 2 x - 5 and 2 x - 5 \leq 3 x$

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 above inequations.

$2 x < - 7 and - 5 \leq x$

$x < - 3.5 and x \geq - 5$

$- 5 \leq x < - 3.5$

As x $\in$ Z, the solution set is {-5, -4 }.

The graphical representation of the solution set on a number line is as follows:

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