Question

Which graph shows the solution set for 2 x + 3 greater-than negative 9?
A number line going from negative 8 to positive 2. An open circle is at negative 3. Everything to the left of the circle is shaded.
A number line going from negative 8 to positive 2. An open circle is at negative 3. Everything to the right of the circle is shaded.
A number line going from negative 8 to positive 2. An open circle is at negative 6. Everything to the left of the circle is shaded.
A number line going from negative 8 to positive 2. An open circle is at negative 6. Everything to the right of the circle is shaded.

Answer 1

To solve the inequality \( 2x + 3 > -9 \), we first isolate \( x \).

1. Subtract 3 from both sides:
\[
2x > -9 - 3
\]
\[
2x > -12
\]

2. Divide both sides by 2:
\[
x > -6
\]

This means the solution set is all numbers greater than \(-6\).

Now, referencing the graph descriptions provided:

1. An open circle at \(-3\) with shading to the left: This represents \( x < -3\).
2. An open circle at \(-3\) with shading to the right: This represents \( x > -3\).
3. An open circle at \(-6\) with shading to the left: This represents \( x < -6\).
4. An open circle at \(-6\) with shading to the right: This represents \( x > -6\).

The correct graph that represents the solution \( x > -6 \) is the last option:

**An open circle at -6 with everything shaded to the right.**