Question

Which one of the following inequality is represented on this number line?


Note: In a number line, a closed circle on the number gets included in the solution, while an open circle on the number will not get included in the solution.

• A. $-3\le x<4$
• B. $-3\le x\le 4$
• C. $-3<x\le 4$
• D. $4\le x<-3$

Answer 1

The correct option is C $-3<x\le 4$

There is a closed circle at 4 with the line showing the numbers that are less than or equal to 4.

This means $x\le 4$ (writing the $x$ on the left-hand side).

There is also an open circle at -3, with the numbers greater than -3 indicated. This means $x>-3\text{or}-3<x$
(writing the $x$ on the right-hand side).

The line between these two points means that $x$ satisfies both the inequalities, so a double inequality must be created.
$-3<x$ and $x\le -4$

Combining both the inequalities gives $-3<x\le 4.$

$\text{Hence,}x\text{is greater than}-3\text{and}x\text{is less than or equal to}4.$