Question

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

Answer 1

`[-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]`