Absolute Value Inequality

[dajanney]

Typical adult garter snakes range in length from 46 to 130 centimeters. Write an absolute value inequality that represents the range of lengths of adult garter snakes.

I set this up as:
Ix + 46I <= 130

If x is a negative number, then the answer is less than 130, but not necessarily >= 46. How do you write the equation to be >=46 AND <=130?

 

[lookagain]

Typical adult garter snakes range in length from 46 to 130 centimeters.
Write an absolute value inequality that represents the range of lengths of adult garter snakes.

I set this up as:
Ix + 46I <= 130

If x is a negative number, then the answer is less than 130, but not necessarily >= 46.
How do you write the equation to be >=46 AND <=130?

You want the average of these numbers, \(\displaystyle 88\).

\(\displaystyle 46 \le x \le 130\)

It is a distance of \(\displaystyle 42\) away from those two extremes.

\(\displaystyle 88 - 42 \le x \le 88 + 42\)

\(\displaystyle -42 \le x - 88 \le 42\)


\(\displaystyle \boxed{|x - 88| \le 42}\)