Inequalities?

Question

Your answer to those inequalities should have either the form:
b or
xc

where x is a variable and b and c are numbers
l k+9 l < 6

Answer 1

When we do an absolute value problem like this, we take the negative and positive value of the expression inside the absolute value sign. So, this problem is interpreted like this:

|k + 9| < 6 ----> k + 9 > -6 or k + 9 < 6.

The reason we turn the inequality sign around when we find the negative value is because if the inequality doesn't initially contain a negative sign on either side, and we place a negative sign in front of a variable expression or a constant on the other side, we have effectively multiplied that side by -1. Mathematical sense dictates that whenever we multiply or divide one side of an inequality by -1, we must reverse the direction of the inequality sign. Otherwise, we have a situation like this resulting:

x > 5, let x be 6. Then 6 > 5 certainly. Now multiply the variable by -1, resulting in -x > 5. If we still let x = 6, is -(6) greater than 5? Certainly not! So, we must flip the inequality sign so that -x < 5. Then -6 < 5, and a true statement results.

Now, let's solve for k.

k + 9 > -6
k > -6 - 9
k > -15

k + 9 < 6
k < 6 - 9
k < -3

So k < - 3 or k > -15.

We could also write the solution set like this:

-15 < k < -3

In other words, k is a number between -15 and -3 exclusive (i.e. the endpoints, -15 and -3, are not included). Try any of them, and they should result in a true statment.

Answer 2

Eu nao entendi nada doque voce esta falando porem quero deixar o meu abraço!!! Podemos ser amigos?