Inequalities Help

I have ran into confusion about a question:

Is -1.05^n > -4 the same as 1.05^n > 4

because if it isn't, I don't see how this question I am tackling is possible, thanks.

Reply 1

Notnek

Original post by Henwi

I have ran into confusion about a question:

Is -1.05^n > -4 the same as 1.05^n > 4

because if it isn't, I don't see how this question I am tackling is possible, thanks.

E.g.

-3 > -4
3 > 4

So no it's not the same. If you move the left to the right and the right to the left you get

4 > 1.05^n

Reply 2

Henwi

Original post by Notnek

E.g.

-3 > -4
3 > 4

So no it's not the same. If you move the left to the right and the right to the left you get

4 > 1.05^n

Ok thanks for the help on that, so let's say for my question 100(1-1.05^n)/1-1.05 > 6000

When i multiply the 6000 by -0.05 does the sign flip?

Reply 3

Notnek

Original post by Henwi

Ok thanks for the help on that, so let's say for my question 100(1-1.05^n)/1-1.05 > 6000

When i multiply the 6000 by -0.05 does the sign flip?

Yes.

Reply 4

Prasiortle

Original post by Henwi

Ok thanks for the help on that, so let's say for my question 100(1-1.05^n)/1-1.05 > 6000

When i multiply the 6000 by -0.05 does the sign flip?

Yes. In general, whenever you multiply/divide an inequality by a negative number, the sign flips. (Notice also that this means you can't multiply/divide an inequality by a variable for which you don't know whether it's positive or negative, because then you don't know whether the sign will flip. Hence if you wanted to do such a multiplication/division, you would need to split into cases based on whether the thing is positive or negative).