Give+an+example+whose+solution+is+the+empty+set.Set3

Some absolute value inequalities will turn out to be an empty set.

For instance, solve the following problem:

If you solve this problem, you will get to |7-4x| < -2. This is not possible, and therefore the answer to the inequality is an empty set.
 * 7-4x| + 8 < 6

Try the following problems to see which are empty sets:

3x + 7 > 2 or 3x + 7 < -2 3x > -5 or 3x < -9 x > -5/3 or x < -3
 * 3x + 7| > 2

Empty set because the lowest the absolute value of -5x can be is 0, and 0 + 2 will always be more than 1.
 * -5x| + 2 < 1

Empty set because the absolute value of something cannot return a negative number.
 * 4x-3| < -3

The correct answer is the last 2 problems are empty sets because there is no answer for x that can make the inequality true.

1. 3x+7>2 3x+7<-2 3x>-5 3x<-9 x>-5/3 x<-3

2. impossible because a possitive number plus 2 always is greater than 1

3. absolute value cannot equal a negative number -Austin Klein