Inequalities with Absolute Values: Solving the problem

Examples with solutions for Inequalities with Absolute Values: Solving the problem

Exercise #1

Given:

\left|x+4\right|>13

Which of the following statements is necessarily true?

Video Solution

Answer

x>9 o x<-17

Exercise #2

Given:

\left|x-4\right|<8

Which of the following statements is necessarily true?

Video Solution

Answer

-4 < x < 12

Exercise #3

Given:

\left|x+2\right|<3

Which of the following statements is necessarily true?

Video Solution

Answer

-5 < x < 1

Exercise #4

Given:

\left|x-5\right|>-11

Which of the following statements is necessarily true?

Video Solution

Answer

No solution

Exercise #5

Given:

\left|x-5\right|>11

Which of the following statements is necessarily true?

Video Solution

Answer

x>16 o x<-6

Exercise #6

Given:

\left|5x-10\right|>15

Which of the following statements is necessarily true?

Video Solution

Answer

x>5 o x<-1

Exercise #7

Given:

\left|3x+9\right|<18

Which of the following statements is necessarily true?

Video Solution

Answer

-9 < x < 3

Exercise #8

Given:

\left|2x-4\right|<8

Which of the following statements is necessarily true?

Video Solution

Answer

-2 < x < 6

Exercise #9

Given:

\left|2x-1\right|>-10

Which of the following statements is necessarily true?

Video Solution

Answer

For all x

Exercise #10

Given:

\left|4x+12\right|>16

Which of the following statements is necessarily true?

Video Solution

Answer

x>1 o x<-7