Question

Which of the following has a solution set of {x | x = 0}?


(x + 1 < -1) ∩ (x + 1 < 1)
(x + 1 ≤ 1) ∩ (x + 1 ≥ 1)
(x + 1 < 1) ∩ (x + 1 > 1)

Answer 1

Here's the best I can do. I would draw a number line and shade the inequalities. Then see which part intersects and if it is 0, that is the answer.

Answer 2

so id have to what?

Answer 3

Solve all the inequalities.

Answer 4

Duhh yeah you can solve them too. Why didn't I think of that @.@

Answer 5

okay so do i do im confused

Answer 6

For example, here is the first one:

(x + 1 < -1) ∩ (x + 1 < 1)

(x < -2) ∩ (x < 0) These two inequalities have x < - 2 in common, so this is not it.

Answer 7

Now try solving the inequalities in the second choice. What do you get?

Answer 8

i got the 3rd one but i think i messed up on something

Answer 9

Ok, let's solve the inequalities of the third choice ansd see what they have in common.

(x + 1 < 1) ∩ (x + 1 > 1)

In both inequalities, subtract 1 from both sodes to get:

(x < 0) ∩ (x > 0)

The solution of the left inequality is every number less than zero.
The solution of the right inequality is every number greater than zero.
You want the instersection of both solutions.
Do the two solutions have any numbers in common?

Answer 10

i got it :) thank you

Answer 11

You're welcome.