Hey! So I'm horrible when it comes to graphing inequalities, I'm good at solving them, just not graphing them. Could I have some help with this question?
Which inequality matches the graph?
<--|------|------|------|------O
-3 -2 -1 0 1
A. 3x + 1 > 4
B. 3x + 1 ≥ 4
C. 3x + 1 < 4
D. 3x + 1 ≤ 4
Can someone just explain how the graph thing works?
Looks like your little circle is open and your line goes to the left,
so you must be looking at
x < 1
Had it been a solid circle the solution would show
x ≤ 1
You have to know and decide if it is open or closed (solid).
You said you were good at solving them, so which one gave you
that solution?
So it must be D? Am i correct
Of course! I'll explain how to graph inequalities and help you choose the correct inequality for the given graph.
To graph an inequality, you first need to determine whether it is a "greater than" or "less than" inequality. In our case, the graph should have a solid line or a dashed line above or below it, indicating whether the inequality includes or excludes the line itself.
Let's analyze the given graph:
<--|------|------|------|------O
The graph shows a solid dot at -3, which means the point -3 is included in the solution set. The arrow points to the left, indicating that the inequality is "less than." The graph continues to the left indefinitely but does not include the endpoint (-3).
To determine the correct inequality, we need to look at the position of the solid line. Since the line lies below the graph, the inequality is less than or equal to.
Now, let's examine the answer choices:
A. 3x + 1 > 4 (greater than)
B. 3x + 1 ≥ 4 (greater than or equal to)
C. 3x + 1 < 4 (less than)
D. 3x + 1 ≤ 4 (less than or equal to)
From the given graph, we can see that the line is below the points and does not touch them. This means the inequality is "less than." Additionally, the endpoint is not included, so it is not "less than or equal to." Therefore, the correct answer is option C. The inequality that matches the graph is 3x + 1 < 4.
I hope this explanation helps you understand how to graph inequalities and choose the correct corresponding equation! Let me know if you have any further questions.