using (-3< x+5< 8) describe how you know if an inequality is an "and" or an "or" problem.

Question

If you have an absolute value question how do you know if it is an "and" or an "or" problem. 

Answer 1

using (-3< x+5< 8) describe how you know if an inequality is an "and" or an "or" problem.

 

this is an "and" problem because the unknown is on the interval between the end points. x+5 is both < 8 AND > -3.

 

If we have |x-3|>5 it means the distance of x from 3 is more than 5, so x can't be between -5 and 5. here x can be more than 5 OR less than -5, but not both at the same time.

Answer 2

Hi Phyllis;

(x+5) is greater than -3 AND less than 8.

If this is |x+5|, then the absolute value of such is a positive value.  It is greater than -3 AND less than 8.

However, if this is |x+5|, we could also express this is as the absolute value of the positive OR negative result of (x+5).