Which graph below bests represent the solution set for `-2x<=3x+10`?
closed or open point
The given inequality is -2x <= 3x + 10.
To graph this inequality, we can first isolate x by subtracting 3x from both sides:
-2x - 3x <= 10
-5x <= 10
Next, we divide both sides by -5. It is important to remember that when dividing or multiplying both sides of an inequality by a negative number, the direction of the inequality changes:
x >= 10/-5
x >= -2
Now, let's look at the graph options.
Option 1: Closed Point
A closed point on the number line is represented by a shaded dot at -2. This indicates that -2 is included in the solution set. However, the solution to the inequality is x >= -2, which means that -2 is not included. Therefore, this graph does not accurately represent the solution set for the given inequality.
Option 2: Open Point
An open point on the number line is represented by an unshaded dot at -2. This indicates that -2 is not included in the solution set. Since the solution to the inequality is x >= -2, an open point accurately represents the solution set.
Therefore, the graph that best represents the solution set for -2x <= 3x + 10 is the graph with an open point.