Inequalities with Absolute Values: Double absolute value

Examples with solutions for Inequalities with Absolute Values: Double absolute value

Exercise #1

Given:

|a|-|18-9|+|4|<0

Which of the following statements is necessarily true?

Video Solution

Answer

-13 < a < 13

Exercise #2

Given:

||1-4|+3|-|a|<0

Which of the following statements is necessarily true?

Video Solution

Answer

a<-6

Exercise #3

Solve:

\Vert-4+8|-2|-|a|>0

Video Solution

Answer

2>a>-2

Exercise #4

Given:

|a|+||5-1|+3-4|<0

Which of the following statements is necessarily true?

Video Solution

Answer

No solution

Exercise #5

Solve:

|a|-||5-4|-1|>0

Video Solution

Answer

All values of a a

Exercise #6

|a|-\left||\right|5-4+3|-1|-1|<-|a|

Which of the following statements is true?

Video Solution

Answer

-1 < a < 1

Exercise #7

Given:

\Vert-8+7|-|5+3|-1|<|a|

Which of the following statements is necessarily true?

Video Solution

Answer

a>8

Exercise #8

Given:

|-3+|-4+8|-5|+|a|<0

Which of the following statements is necessarily true?

Video Solution

Answer

No solution

Exercise #9

|a|-||8-5|+8-3|>-|a|

Which of the following statements is true?

Video Solution

Answer

a<-4

Exercise #10

Given:

\left||\right|-8-5+4|-1|-3|>|a|

Which of the following statements is necessarily true?

Video Solution

Answer

-5 < a < 5