Question

Which graph below bests represent the solution set for `-2x<=3x+10`?
closed or open point
and is it shaded leeft or right

Answer 1

Closed or open point?

Answer 2

The correct representation for the solution set of `-2x <= 3x + 10` is a shaded region on the graph. To determine if the shaded region is to the left or right, we need to manipulate the inequality.

First, let's isolate the variable `x` by subtracting `3x` from both sides and adding `10` to both sides:

```
-2x <= 3x + 10
-2x - 3x <= 3x + 10 - 3x
-5x <= 10
```

Next, we divide both sides by `-5`. Remember that when dividing or multiplying by a negative number, the inequality direction flips:

```
(-5x)/-5 >= 10/-5
x >= -2
```

Now we can graph this inequality on a number line. Since the inequality is inclusive (`x >= -2`), the point at `-2` will be closed. The shaded region will be to the right of `-2` since the inequality sign points in that direction.

Here is the graphed solution set:

```
-------------------------------------> [number line]
-3 -2 -1 0 ...
*-----|-----|-----|----*
-2 |
shaded region
```

The shaded region is to the right of the point `-2` and represents the solution set for `-2x <= 3x + 10`.

Answer 3

The point at `-2` on the number line is a closed point. In the graph of the solution set, there is a solid dot at `-2`. A solid dot represents a closed point because it includes the value `-2` as part of the solution.