Question

What is the solution set of –x2 – 6 < 0?

Answer 1

the answer is the longer one with parenthesis

Answer 2

The solution set for the inequality ,
`-x^2-6<0` is every real number
`x`. There are two ways to understand why every real number
`x` is a solution to this inequality. The first way is to solve this inequality for
`x^2` and then interpret the result. Note that for any real numbers
`a` and
`b`,

`-a<b\\=>a>-b.`

We solve the inequality as follows,

`-t^2-6<0\\=>-t^2<6\\=>t^2>-6.`

This result means that the square of any real number will always be greater that -6. We know this to be true because the square of any number is positive and even the smallest positive number is greater than any negative number.

The other way to solve this inequality would be to draw the graph of the inequality. This graph should be below the
`x`-axis for all values of
`x`. Such a graph is shown in the image attached.