What is the solution to the inequality #absx≤7#?

1 Answer
Sep 1, 2015

Answer:

#[-7,7]#

Explanation:

There are two possibilities:

Either x is greater than 0, in which case #x <= 7#

Or, x is less than 0, in which case #x >= -7# (because in order for the absolute value of x to be less than 7, x must be greater than -7.)

So, x has to be less than or equal to 7, and x has to be greater than -7. So, the solution set will be "from -7 to 7, inclusive". This can be written like this:

#[-7, 7]#