Write each compound inequality as an absolute value

Maria Nava

Maria Nava

Answered question

2022-09-20

Write each compound inequality as an absolute value inequality

 

-2 < x < 2

Answer & Explanation

Mr Solver

Mr Solver

Skilled2023-05-25Added 147 answers

To write the compound inequality 2<x<2 as an absolute value inequality, we can break it down into two separate inequalities and then combine them using the absolute value notation.
First, let's focus on the lower bound: 2<x. This means that x is greater than -2. We can write this inequality as:
x>2
Now let's consider the upper bound: x<2. This indicates that x is less than 2. We can express this inequality as:
x<2
To combine these two inequalities using absolute value notation, we can use the concept that the absolute value of a number represents its distance from zero on the number line. In this case, we want to find the range of values of x that are within a certain distance from zero.
To represent the distance from zero, we can use the absolute value of x, denoted as |x|. To ensure that the distance from zero is less than 2, we can write:
|x|<2
Combining all the information, we can express the given compound inequality 2<x<2 as an absolute value inequality:
|x|<2
This inequality states that the absolute value of x is less than 2, indicating that x can be any real number within a distance of 2 units from zero on the number line, excluding the endpoints -2 and 2.

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