Question

Does anybody know inequalities?

Answer 1

Whatcha got?

Answer 2

d - 1 > -3 and d + 2 < 5

-3k + 7 > -5 and -7k + 5 < -2

-5 < 2y - 3 < 23

x - 4 < 5 or x + 2 > 15

5x - 4 > 6 or -4x + 5 > 1

Answer 3

Just solve for the variables?

Answer 4

Or are we graphing?

Answer 5

Graphing.. :c

Answer 6

Gotcha. Well, the first thing to point out is the difference between "or" and "and."

When we have "and" the numbers we find have to make both inequalities true.
When I say make both inequalities true, I mean that if we have something like x <4 and
x > 2. Well, if I have the number x = 5, then it only makes one of these two inequalities true. So that means I cannot use that point.

When we have "or", this means I only need one inequality to be true. So if I use the same inequalities, x = 5 is trueforone of the two, so that means I can use that point. So there is a big difference with those words. So now to actually get to a problem, lol. The first problem is
d-1 > -3 and d + 2 < 5
We have the word and, so we must have values of d that make both inequalities true. Make sense so far?

Answer 7

Yes

Answer 8

Okay, so the first problem is easy to solve for d. For the first inequality I can add 1 to both sides and get d > -2. The second one I can simply subtract 2 from both sides to get d < 3. So now comparing the two inequalities
d > -2
d < 3
There's no context to say whether this would be the same as x or y, so I'll just get a number line solution for it and you can tell me if I need to do more. So we have less than and greater than but no equal to bar underneath them. This means that on a graph i would have to use a dashed line and on a number line I use parenthesis. Since this question was "and", I only want parts of the number line where these solutions overlap, so that will giveme this: