solve the inequality. |7x|>28.

Question

Solve the inequality.  |7x| > 28

Answer 1

Hi again Kevin;

|7x| > 28

You may or may not already know that > means that |7x| must be greater than 28.  When I was in sixth grade, we remembered this as, the alligator is going to eat the bigger one.

 

We need to establish the values which would render this acceptable to the alligator.

 

You probably already know that the symbols | | mean absolute value.  This means that x can be either positive or negative, and the result will be the same in the positive range of numbers.

Let's begin with...

7x=28

x=4

Because we are considering absolute value...

x=-4

This would originally render 7x as -28.  Because it is absolute value, it conclusively is 28.

 

The domain of x is...

(negative infinity, -4)U(4, positive infinity)

The parentheses indicate that neither -4 nor positive 4 are part of the union because this is >, values which are only greater than.  It is not greater than or equal to, ≥, which would include -4 and 4.

 

Answer 2

In addition to Vivian answer : 

(- ∞, -4) U (4, +∞) 

  <====|====o------|------o====|====>  
 - ∞    - 10      - 4       0        4        10     + ∞


Let's verify the answer: 

if x = - 10, then
|7*(- 10)| > 28 
    70 > 28  True 

if x = 0, then 
|7*0| > 28 
   0 > 28 False 

if x = 10, then 
|7 * 10| > 28 
    70 > 28  True