Trigonometry_ Ice Cream life: The weird FIRST time

MY FIRST POST(yay!^.^)

Hello, everyone :D

this is the second blog about math D;

(Yea,yea) we all hate math like typical teenagers, but I have to do it because of my teacher :(

but enough of introductions

its the dreading time (tan,tan,tan)

Trigonometry Time

Question:

"Why do we flip the inequality symbol when multiplying by a negative number or solving absolute value inequalities?"

okay, so here we go ^.^ on our foot journey:)...

For example, if we had a statement like: 20 > 12 then it would be true, but lets say that that you are told to multiply both numbers by a negative number ?

what do we do now ?? :O

have no fear I will explain :)

In my example,we will multiply each side by -2.

20(-2) < 12(-2)

your outcome will be:

-40 > -24 and this is false because -40 is lesser than -24

To make it clear I made a number line ---->

In a number line, the positive numbers show amount of value by having the numbers closer to zero value less while the numbers father away from zero have a greater value.

But for the left side of the number line if the numbers are closer to zero then their amount of value higher than the numbers father away from zero.

therefore if -42 is more farther from zero then it has a lesser value than -24 since it is much more closer.

Back to our problem, if : -42 > -24

it would be incorrect because like we said before -42 has a lower value than -24 because it is the more farther away than -24.

DO YOU GET IT NOW?

So, we change the sign to number one : have the correct sign when dealing with negative numbers

In absolute inequalities you change the sign for the same reason

for example :

I2x+1I >6

you would first make two separate equations

like:

2x+1>6 and 2x+1<-6.

2x+1>6 :

In this case we are saying that 2x+1 is greater than 6

2x+1<-6

In this equation we switched the sign and made the 6 negative, because from the previous equation we only had the answer of a full set of positive numbers not the negative numbers .