Which region does the constraint 2x + 3y ≤ 12 describe?

Question 18

EasyOriginal question

Which region does the constraint $2x + 3y \le 12$ describe?

The line

2x + 3y = 12

and the side of it away from the originCorrect answerYour answerOnly the points of the line

2x + 3y = 12

Correct answerYour answerThe line

2x + 3y = 12

and the side of it that contains the originCorrect answerYour answerOnly the points with

x \le 6

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

A linear inequality describes a half-plane: the boundary line and everything on one side of it.
Test the origin: $2(0) + 3(0) = 0 \le 12$ is true, so the side with the origin is the one shaded.

Worth noting

The far side is the region of $2x + 3y \ge 12$ .

Ten questions from Linear Programming, at your own pace.