Find an equivalent inequality with absolute value
#1: -5 < y < 5
#2: x < -4 or 4 < x
I'm not sure at all how to solve this problem. Please walk me through the process.
Thanks!
To find an equivalent inequality with absolute value, we need to express the given inequality using absolute value notation.
Let's start with the first inequality: -5 < y < 5.
To express this inequality using absolute value, we can consider that y must be within a certain distance from zero. Since the inequality represents y being between -5 and 5, it means the distance between y and zero should be less than 5. Thus, we can write this inequality as:
|y - 0| < 5.
This notation indicates that the absolute value of the expression inside the brackets (y - 0) should be less than 5.
Now, let's move on to the second inequality: x < -4 or 4 < x.
We can approach this inequality in a similar way. Here, x is either less than -4 or greater than 4. This means that the distance between x and zero should be greater than 4. Therefore, we can write this inequality as:
|x - 0| > 4.
This notation indicates that the absolute value of the expression inside the brackets (x - 0) should be greater than 4.
In summary, the equivalent inequalities with absolute value are:
#1: |y - 0| < 5.
#2: |x - 0| > 4.