Question

the movement of the progress bar may be uneven because questions can be worth more or less (including zero). solve |2x + 5| < 11 and graph the solutions.
-8 < x < 3

x > -8 or x < 3

x > -8 and x < 3
no solutions

x < -8 or x > 3

Explanation:

Step1: Recall absolute inequality rule

For \(|a| < b\) (\(b>0\)), it is equivalent to \(-b < a < b\). So for \(|2x + 5| < 11\), we get \(-11 < 2x + 5 < 11\).

Step2: Subtract 5 from all parts

Subtract 5: \(-11 - 5 < 2x + 5 - 5 < 11 - 5\), which simplifies to \(-16 < 2x < 6\).

Step3: Divide by 2

Divide each part by 2: \(\frac{-16}{2} < \frac{2x}{2} < \frac{6}{2}\), so \(-8 < x < 3\) (or \(x > -8\) and \(x < 3\)). The graph has open circles at -8 and 3, with a line between them.

Answer:

The correct option is the first one: \(-8 < x < 3\) with the graph having open circles at -8 and 3 and a line connecting them (the first graphical option shown).