The absolute value inequality |x-3y| > 2 is equal to what pair of linear inequalities?

Question

I don't know if the answer is "and" or "or" either....

Answer 1

Rule of thumb: when you're dealing with a less than symbol (or, in actuality, less than symbol OR less than or equal symbol), you will be dealing with an AND.

Example:

|x| < 6 is the same as -6 < x < 6
|x - 3| <= 5 is the same as -5 <= x - 3 <= 5

Whenever you're dealing with a greater than, or greater than or equal symbol, you will be dealing with an OR.

Example:

|x| > 6 is the same as x > 6 OR x < -6
|x - 3| >= 5 is the same as x - 3 >= 5 OR x - 3 <= -5


Now for your question,

|x - 3y| > 2 is the same as

[x - 3y > 2] OR [x - 3y < -2]

If we wanted, we can actually solve these inequality such that y is on the left hand side. Using algebra, you'll ultimately come up with these linear inequalities:

x - 3y > 2
-3y > - x + 2

Since dividing by a negative number in an inequality switches the sign, that's what happens.

y < (1/3)x - (2/3)

x - 3y < -2
-3y < -x - 2

y < (1/3)x + (2/3)

Two linear inequalities:

y < (1/3)x - (2/3)
y < (1/3)x + (2/3)

Now for something totally off topic:

If you're ever given the equation
|x| > -2
This is something which is ALWAYS going to be true, because the absolute value of a number is ALWAYS greater than or equal to 0. The solution set for x would be all real number.

For |x| < -2, you'll get no solution.

Answer 2

the way we do it here is :

x- 3y =2 and x -3y = -2
then if you want the answer is slope intercept form, all you need to do is solve for y.

any time the inequality is a greater or " greater or equal" then those are and problems. Less or "less or equal" are or problems. I hope this helps.

Answer 3

i actually had a test on this today. so you know the v is for absolute value right? so just draw the original one which is on the point (0,0) +3 shows it goes up 3 so it is the point 0,3 the 2 show streches vertically 2 i'm sure about everything :)

Answer 4

Well either x-3y is positive or it is negative.

Therefore x-3y>2 (positive case), OR -(x-3y)>2 (negative case).

You can work out the rest.

Answer 5

x-3y>2
or -x+3y<2