Question

Which option represents the inequality $1\le 2x+5<15$ on the 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.
• B.
• C.
• D.

Answer 1

The correct option is B

Given, $1\le 2x+5<15$

Step 1: Subtract each side of the inequality by 5.
Also, subtracting the same number from each side of an inequality does not change the direction of the inequality.
$\Rightarrow 1-5\le 2x+5-5<15-5\Rightarrow -4\le 2x<10$

Step 2: Divide each side of the inequality by 2.
Also, dividing a positive from each side of an inequality does not change the direction of the inequality.
$\frac{-4}{2}\le \frac{2x}{2}<\frac{10}{2}$
$-2\le x<5$
The symbol used is ''less than or equal to'' $(\le )$ so a closed circle must be used at -2, which means -2 is included in our solution.

And for ''less than'' $(<)$ symbol, an open circle must be used at 5, which means 5 is not included in our solution.

So, $x$ is greater than or equal to -2 and less than 5.

Hence, is the correct option.