Question

which graph shows the solution set for (2x + 3 > -9)?
(\boldsymbol{circ}) (overleftarrow{
ule{2cm}{0.1em}}) (circ) (-8) (-7) (-6) (-5) (-4) (-3) (-2) (-1) (0) (1) (2)
(\boldsymbol{circ}) (cdots) (circ) (overrightarrow{
ule{2cm}{0.1em}}) (-8) (-7) (-6) (-5) (-4) (-3) (-2) (-1) (0) (1) (2)
(\boldsymbol{circ}) (overleftarrow{
ule{2cm}{0.1em}}) (circ) (-8) (-7) (-6) (-5) (-4) (-3) (-2) (-1) (0) (1) (2)
(\boldsymbol{circ}) (cdots) (circ) (overrightarrow{
ule{2cm}{0.1em}}) (-8) (-7) (-6) (-5) (-4) (-3) (-2) (-1) (0) (1) (2)

Explanation:

Step1: Solve the inequality for x

We start with the inequality \(2x + 3>-8\). First, we subtract 3 from both sides of the inequality.
\(2x+3 - 3>-8 - 3\)
Simplifying both sides, we get \(2x>-11\). Then, we divide both sides by 2 to solve for x.
\(x>-\frac{11}{2}\)
\(-\frac{11}{2}=- 5.5\)? Wait, no, wait. Wait, let's recalculate. Wait, \(-8-3=-11\), then \(2x>-11\), so \(x>-\frac{11}{2}=-5.5\)? Wait, no, wait the original inequality is \(2x + 3>-8\)? Wait, maybe I made a mistake. Wait, let's do it again.

Wait, the inequality is \(2x + 3>-8\). Subtract 3 from both sides: \(2x>-8 - 3=-11\). Then divide by 2: \(x>-\frac{11}{2}=-5.5\)? Wait, but looking at the number lines, the options have -6, -5, etc. Wait, maybe the original inequality is \(2x + 3>-9\)? Wait, the user wrote \(2x + 3>-8\)? Wait, maybe it's a typo, but let's check the number lines. Wait, the first option has an open circle at -3, the second at -3, third at -6, fourth at -6. Wait, maybe the inequality is \(2x+3>-9\). Let's assume that maybe it's a typo. Let's re - solve \(2x + 3>-9\).

Subtract 3: \(2x>-9 - 3=-12\). Divide by 2: \(x>-6\). Ah, that makes sense with the number lines. Maybe the original problem was \(2x + 3>-9\). Let's proceed with that (since the number lines have -6 as a key point).

So, if we solve \(2x+3>-9\):

Step1: Subtract 3 from both sides

\(2x+3 - 3>-9 - 3\)
\(2x>-12\)

Step2: Divide both sides by 2

\(\frac{2x}{2}>\frac{-12}{2}\)
\(x>-6\)

Now, to graph \(x > - 6\), we use an open circle at \(x=-6\) (because the inequality is strict, \(>\) not \(\geq\)) and draw an arrow to the right (since we want all values greater than -6).

Looking at the options:

• The first option: Open circle at -3, arrow left. Not correct.
• The second option: Open circle at -3, arrow right. Not correct.
• The third option: Open circle at -6, arrow left. Not correct (we need arrow right for \(x > - 6\)).
• The fourth option: Open circle at -6, arrow right. This matches our solution \(x>-6\).

Answer:

The fourth graph (the one with an open circle at -6 and an arrow pointing to the right)