Solve the inequality. |7x| > 28

## solve the inequality. |7x|>28.

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# 2 Answers

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.

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