# Thread: (int. Algebra) Inequality result question.

1. ## (int. Algebra) Inequality result question.

Hello all,

Just when I thought I completely understood union and intersection, I ran into something that I just can't figure out.

Given: $\displaystyle x\geq -2\text{ or } x \geq 5$

I get the solution: $\displaystyle [-2,\infty)$

But when replace the "or" with an "and" $\displaystyle x\geq -2\text{ and } x \geq 5$, I assume the solution is
$\displaystyle [5,\infty)$. Is this correct? If not, why?

Thank you

2. ## Re: (int. Algebra) Inequality result question.

Yes, that is correct. In the first case, you are told that $\displaystyle x\ge -2$ or $\displaystyle x\ge 5$. That is, x could satisfy either one of those inequalities. For example, x= 1 would satisfy that. Even though it does not satisfy $\displaystyle x\ge 5$, it does satisfy $\displaystyle x\ge -2$. Of course, any number greater than or equal to 5 is greater than or equal to -2 so it is enough to say $\displaystyle x\ge -2$.

On the other hand, if we are told that $\displaystyle x\ge -2$ and $\displaystyle x\ge 5$, x must satisfy both inequalities. x= 1 would not satisfy this- it does not satisfy $\displaystyle x\get 5$. Of course, again, any number greater than or equal to 5 is greater than or equal to -2 so it is enough to say $\displaystyle x \ge 5$.