Question

If $x$ satisfies the given inequality below, then
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. $x\text{is greater than or equal to}4\text{and}x\text{is less than or equal to}9.$
• B. $x\text{is greater than}4\text{and}x\text{is less than or equal to}9.$
• C. $x\text{is greater than or equal to}4\text{and}x\text{is less than}9.$
• D. $x\text{is greater than}4\text{and}x\text{is less than}9.$

Answer 1

The correct option is A $x\text{is greater than or equal to}4\text{and}x\text{is less than or equal to}9.$

There is a closed circle at 9 with the line showing the numbers that are less than or equal to 9.

This means $x\le 9$ (writing the $x$ on the left-hand side).

There is also a closed circle at 4, with the numbers greater than or equal to 4 indicated. This means $x\ge 4\text{or}4\le x.$
(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.
$4\le x$ and $x\le 9$

Combining both the inequalities gives $4\le x\le 9.$

$\text{Hence,}x\text{is greater than or equal to}4\text{and}x\text{is less than or equal to}9.$