Question

which number line represents |2x + 1| < 5?

Explanation:

Step1: Remove the absolute - value

The inequality \(|2x + 1|\lt5\) is equivalent to \(- 5\lt2x + 1\lt5\).

Step2: Subtract 1 from all parts

Subtracting 1 from each part of \(-5\lt2x + 1\lt5\) gives \(-5-1\lt2x+1 - 1\lt5 - 1\), which simplifies to \(-6\lt2x\lt4\).

Step3: Divide by 2

Dividing each part of \(-6\lt2x\lt4\) by 2 gives \(\frac{-6}{2}\lt\frac{2x}{2}\lt\frac{4}{2}\), so \(-3\lt x\lt2\).
On a number - line, this is represented by an open - circle at \(x=-3\) and \(x = 2\) and a line segment connecting them.

Answer:

The number - line with open - circles at \(x=-3\) and \(x = 2\) and a line segment between them (the third option among the ones presented if they follow the described pattern).