How do you graph the inequality 6x + 3y > 12?
Solution:
The graph is plotted below and the inequality indicated:
The arrows indicate the area which satisfies the inequality 6x + 3y > 12. The inequality suggests that the points on the line 6x + 3y = 12 are not included in the inequality.
The inequality region 6x + 3y > 12 is ascertained by taking points on either side of the line and substituting in the inequality to verify.
How do you graph the inequality 6x + 3y > 12?
Summary:
The inequality 6x + 3y > 12 is first graphed by first drawing the line 6x + 3y = 12 and then verifying which points on either side of the line satisfy the inequality. Accordingly, the relevant region is shaded as shown in the solution.
- Let us take a point (2, -2) which is below the line 6x + 3y = 12. Substituting x= 2 and y = -2 we get 12 - 3(-2) > 12 is incorrect hence the area below the line does not satisfy the inequality.
- Let us take a point above the line (4, 0) and substitute in the inequality 6(4)+ 3(0) > 12 is correct. Hence the area above the line satisfies the inequality. Hence the area above is shaded with arrows