Question

-1 < 2x + 5 < 15
graph the solution on the number line.
number line with markings from -11 to 11, open circles at -3 and 5, and a line segment between them

Explanation:

Step1: Subtract 5 from all parts

To solve the compound inequality \(-1 < 2x + 5 < 15\), we first subtract 5 from each part of the inequality. This is done to isolate the term with \(x\).
\[
-1 - 5 < 2x + 5 - 5 < 15 - 5
\]
Simplifying each part:
\[
-6 < 2x < 10
\]

Step2: Divide all parts by 2

Next, we divide each part of the inequality by 2 to solve for \(x\).
\[
\frac{-6}{2} < \frac{2x}{2} < \frac{10}{2}
\]
Simplifying each part gives:
\[
-3 < x < 5
\]

To graph this on the number line, we use open circles at \(x = -3\) and \(x = 5\) (since the inequality is strict, \(x\) cannot be equal to -3 or 5) and draw a line segment between them to represent all the values of \(x\) that satisfy the inequality.

Answer:

The solution to the inequality \(-1 < 2x + 5 < 15\) is \(-3 < x < 5\). The graph on the number line has open circles at \(-3\) and \(5\) with a line connecting them.