00:01
So for this problem, we're given this compound inequality.
00:04
In order to graph it, we have to graph the inequalities individually.
00:08
So let's start with the first one.
00:11
We have to convert the inequality into an equation.
00:15
So 3x plus 2y equals 6.
00:19
Now we have to find both the x intercept and the y intercept.
00:24
To find the x intercept, you make y equal to 0.
00:27
So you insert the 0 wherever the y is in the equation.
00:31
And you get 3x equals 6.
00:34
You solve for x and you get x equals 2.
00:37
Now you plot this point onto the graph.
00:41
So when y is 0, x is 2.
00:44
Now to find the y intercept, you have to make x equal to 0, and you insert the x 0 into wherever the x is in the equation, and you get 2y equals 6.
00:55
When you solve for y, you get y equals 3.
00:59
Now you plot this one, when x is 0, y equals 3.
01:05
Now when you connect both these points that'll give you the boundary line.
01:10
Before that you have to look at the sign in the inequality.
01:13
Since this is a less than sign, we know that the boundary line will be a dotted, a dash line.
01:22
So you just draw the dash line and this is the boundary line for this first inequality.
01:28
Now we have to determine which side we shade if it's under the line or above the boundary line.
01:34
We do this by using a test point.
01:38
You could use 0 comma 0 for this one.
01:40
Now we just insert these values into the inequality to see if it holds true.
01:46
So 3 times 0 plus 2 times 0 less than 6.
01:52
When you saw for this, is 0 less than 6? yes...