How do you know if your question is a "and" or "or" inequalities/compound inequalities?

Question

Thanks!

Its it:

if the sign is < then it is an "and"

if the sign is > then is is an "or"

right? or wrong?

Answer 1

Questions are normally "and"; answers may be "and" or "or".

If you have a chain of inequalities such as
0 < x < 3-2x < 2
then these are to be read as
0 < x and x < 3-2x and 3-2x < 2
=> x > 0 and x < 1 and 2x > 1
=> x > 1/2 and x < 1

"Or" situations usually arise from products or absolute values:

x(3-x) > 0
=> (x > 0 and 3-x > 0) OR (x < 0 and 3-x < 0)
=> (x > 0 and x < 3) OR (x < 0 and x > 3)
In this case the second bracket is impossible so we are left with (x > 0 and x < 3).

With absolute values, an absolute value being less than a given number gives you an "and" inequality, but an absolute value being greater than a given inequality gives you an "or":

|x-7| < 3
=> x-7 > -3 and x-7 < 3
=> x > 4 and x < 10

|x-7| > 3
=> x-7 < -3 or x-7 > 3
=> x < 4 or x > 10


NOTE: Nature Nate's answer is wrong. His example of 3>x>5
is still an "and" inequality. This one has no solutions (because there is no overlap on the number line between 3 > x and x > 5).

Answer 2

split it up and draw each part on a numberline. if there is an area of overlap, it is an "and". if there is no overlap, then it is an "or"

for example, let's take 3>x>5
split this to be 3>x and x>5
when graphed on a number line, there will be two arrows heading away from each other, and a space inbetween. so this would be an "or"

if we had 33) and x<5
when we graph this, the arrows head towards each other and overlap for a time (between 3 and 5). so this would be an "and"

hope this helps

Answer 3

It's not as simple as < being an "and" and > being an "or".

Take this statement:

3 < x < 5

This translates into "x is between 3 and 5"; i.e

3 < x AND x < 5