Which graph shows the solution set for
?
The Correct Answer and Explanation is:
We are given the inequality:
2x + 3 > -9
Let’s solve it step by step:
Step 1: Subtract 3 from both sides:
2x+3−3>−9−32x>−122x + 3 – 3 > -9 – 3 \\ 2x > -12
Step 2: Divide both sides by 2:
x>−6x > -6
So, the solution set is all real numbers greater than -6, which we write as: x>−6x > -6
Step 3: Graph interpretation
We are looking for a number line graph that:
- Has an open circle at -6 (because the inequality is strict, not ≥).
- Has a ray pointing to the right, indicating all numbers greater than -6.
Analysis of the given graphs:
- Option A: Open circle at -6, arrow pointing left → Incorrect (this represents x<−6x < -6)
- Option B: Closed circle at -6, arrow right → Incorrect (represents x≥−6x \geq -6)
- Option C: Open circle at -6, arrow right → Correct (represents x>−6x > -6)
- Option D: Closed circle at -6, arrow right → Again, represents x≥−6x \geq -6 → Incorrect
✅ Correct answer: Option C
Explanation
The inequality given is 2x+3>−92x + 3 > -9. To solve this, we isolate the variable xx. First, subtract 3 from both sides to get 2x>−122x > -12. Then divide both sides by 2, resulting in x>−6x > -6. This means that the solution includes all numbers greater than -6 but not -6 itself.
In graphing inequalities on a number line, an open circle represents values not included in the solution (for strict inequalities like > or <), while a closed circle represents values included (for ≥ or ≤). Since -6 is not part of the solution, we must use an open circle at -6. Additionally, since the inequality is “greater than,” we shade or draw an arrow to the right of -6, representing all values larger than -6.
Only Option C meets both of these criteria: an open circle at -6 and a ray extending to the right. The other options either point the wrong way or include -6, which changes the meaning of the inequality. Therefore, Option C is the correct graphical representation of the solution set to the inequality 2x+3>−92x + 3 > -9.
