Question

Graph the linear inequality.

x < - 6
Answer
Graph the inequality.


x + 4y > 8
Answer
are you sure?
Answered by GPT 3.5
To graph the linear inequality x < -6, we need to draw a dotted line at x = -6 because the inequality is strict (less than). Then, since x is less than -6, all the points to the left of the line will satisfy the inequality.

Here is the graph of the linear inequality x < -6:

( -10, 0) ─┐
│
│
│
│
│
│
└──────────( 5, 0)

The shaded region indicates all the points that satisfy the inequality x < -6.
Answered by GPT 3.5
To graph the inequality x + 4y > 8, we first need to graph the line x + 4y = 8.

To do this, we rearrange the equation to solve for y:

4y = -x + 8
y = (-1/4)x + 2

Next, we plot the y-intercept at (0, 2) and find another point by using the slope of -1/4. Since the slope is negative, we move down 1 unit and to the right 4 units: (4, 1).

Now, we draw the line that passes through these two points:

│
│
│
│
──┼─────────────────────────
│
│
│
│

Next, we determine which side of the line to shade in order to represent the inequality x + 4y > 8. Since the inequality is greater than (not equal to), the shaded area will be above the line.

Finally, we shade the area above the line:

│ A
│ │
│ │
│ │
──┼───────A──────────────┈
│ │
│ ↑│
│ │
Answered by GPT 3.5
Apologies for the confusion. I made a mistake in the previous response. Let me correct it.

To graph the inequality x + 4y > 8, we can first graph the line x + 4y = 8 by finding two points on the line.

Setting x = 0, we find y = 2. Therefore, the point (0,2) is on the line.
Setting y = 0, we find x = 8. Therefore, the point (8,0) is on the line.

Now, we can draw the line that passes through these two points:

│
│
───────┼───
│
│
From the equation x + 4y > 8, we know that any point above this line will satisfy the inequality. However, since the inequality is not equal to, we need to use a dashed line to represent it.

Finally, we shade the region above the dashed line:

↑ A
\│/
─
(