Match the inequality to its graph.
- 1.5 * d >= 9
O A
O B
O C
O D
O C
To match the inequality to its graph, we need to solve the equation and identify which graph represents the solution.
Let's solve the inequality -1.5d ≥ 9:
First, we divide both sides of the inequality by -1.5 to isolate d:
d ≤ 9 ÷ -1.5
This simplifies to:
d ≤ -6
Now that we have the solution d ≤ -6, let's look at the graphs and see which one represents this inequality. Unfortunately, I cannot provide visual representations, but you can refer to the graphs labeled A, B, C, and D and consider their positions on the number line:
- Graph A represents d > -6
- Graph B represents d ≤ -6
- Graph C represents d < -6
- Graph D represents d ≥ -6
From the options given, the correct graph for the inequality -1.5d ≥ 9 is Graph B.
To match the inequality -1.5*d ≥ 9 to its graph, we need to understand the steps to graph inequalities.
Step 1: Start by solving the inequality for d.
To solve -1.5*d ≥ 9, we can begin by dividing both sides of the inequality by -1.5, but we need to remember to flip the direction of the inequality symbol when dividing by a negative number:
d ≤ 9 / -1.5
Simplifying this expression gives us:
d ≤ -6
Step 2: Graph the inequality on a number line.
To graph the inequality d ≤ -6, we plot a closed point (◼) at -6 and shade the region to the left of that point.
Example graph:
____________________________________________________
-10 -9 -8 -7 -6 -5 -4 -3
⬤◼─────────────────────────────────────────────
The shaded region on the number line represents all values of d that satisfy the inequality -1.5*d ≥ 9.
Now, we can match the inequality -1.5*d ≥ 9 to its graph.
The correct match is:
O B