Question

which graph shows the solution set for (2x + 3 > -9)?

Explanation:

Step1: Solve the inequality for x

Subtract 3 from both sides of the inequality \(2x + 3 > -9\):
\(2x + 3 - 3 > -9 - 3\)
Simplify: \(2x > -12\)

Step2: Divide by 2

Divide both sides by 2:
\(\frac{2x}{2} > \frac{-12}{2}\)
Simplify: \(x > -6\)

Step3: Analyze the number line

The solution \(x > -6\) means we have an open circle at \(-6\) (since \(x\) is not equal to \(-6\)) and the arrow points to the right (for values greater than \(-6\)).

Looking at the options, the fourth graph (with open circle at \(-6\) and arrow right) matches this.

Answer:

The fourth graph (with open circle at -6 and arrow pointing to the right, i.e., the option with the open circle at -6 and the line shaded to the right from -6)