Is This Right?

[Tig27]

2x<(or equal to)4 OR 5x-20>(or equal to)5

Basically I get x>(or equal to)-2 or x(or equal to)5

so I guess you have to write it in the union, right?

So I put [-2,∞) U [5,∞)

 

[Tig27]

Actually it's not since the answer is only (2,∞). But my question is how do I know when it's going to be a union and when it's not. I know the or, will give me a indication that it could be, but for example this one wasn't. And for example x+4<0 or 6x-12 is a union when you write it out like this (-∞,4) u (-2,∞).

 

[lookagain]

2x<(or equal to)4 OR 5x-20>(or equal to)5

\(\displaystyle 2x \le 4 \ \ or \ \ 5x - 20 \ge 5\)

\(\displaystyle x \le 2 \ \ or \ \ x \ge 5\)

\(\displaystyle (-\infty, 2] \cup [5, \infty)\)



Basically I get x>(or equal to)-2 or x(or equal to)5



so I guess you have to write it in the union, right?



So I put [-2,∞) U [5,∞)

Tig27,

did you leave out/copy wrong any negative signs for the first inequality?

 

[HallsofIvy]

2x<(or equal to)4 OR 5x-20>(or equal to)5

Basically I get x>(or equal to)-2 or x(or equal to) 5

that is correct if the inequality was \(\displaystyle -2x\le 4\).

so I guess you have to write it in the union, right?

So I put [-2,∞) U [5,∞)

which is the same as [-2,∞) since [5,∞) is a subset of [-2,∞).

The way you decide whether to use "union" or "intersection" is to look at their definitions:
an object is in A union B if it is in in A or in B. It is in A intersection B if it is A and B. This problem said "or" so it is the union of the two sets. But, as I said, one is a subset of the other so the union is just the larger set. If the problem had been \(\displaystyle -2x\le 4\) and \(\displaystyle 5x- 20\le 5\) the solution set would be the intersection which, since one is a subset of the other, would be the smaller.