Graph the absolute value inequalities.
I just can not get this. Please help!
x + 2y ¡Ý 6
To graph the absolute value inequality, follow these steps:
1. Start by graphing the related equation. In this case, graph the equation x + 2y = 6. This will give you a line on the coordinate plane.
2. Next, choose a test point that is not on the line. Any point will do, as long as it is not on the line. Let's say you choose (0,0).
3. Substitute the x and y values from the test point into the original inequality x + 2y ≥ 6. This will tell you whether the inequality is satisfied or not.
Substitute x = 0 and y = 0: 0 + 2(0) ≥ 6
Simplify: 0 ≥ 6
Since 0 is not greater than or equal to 6, the test point (0,0) is not a solution and lies outside the shaded region.
4. Now, determine which side of the line to shade based on the inequality symbol. Since the inequality symbol is "≥" (greater than or equal to), you should shade above the line to represent all the points that satisfy the inequality.
5. Finally, draw a shaded region above the line. This shaded region represents the solution to the absolute value inequality.
That's it! You have successfully graphed the absolute value inequality x + 2y ≥ 6.