Question

Inequality

Answer 1

Why is it greater than or equal to 0 and not less than and equal to?

Answer 2

I was saying \[x(x-6)\le0\]
\[x-6\le0\]

Answer 3

Solvin to get x le 6

Answer 4

and x le 0
(le = less than, equal to)

Answer 5

tell me this,

ab \(\le\) 0

Answer 6

does tha tmean, \(a \le 0\) , and b \(\le\) 0 ?

Answer 7

It means the two multiplied together is less than or equal to zero?

Answer 8

yes, so ?

Answer 9

when is that possible ?
the product ab to be le 0

Answer 10

is it possible when both a & b are negative ?

Answer 11

One would have to be negative and the other positive. Otherwise it would be greater than?

Answer 12

yup ! a & b both positive also wont work

Answer 13

How do you know which one which on the original ??

Answer 14

lets go back to ur original problem and see :)

Answer 15

\(x(x-6)\le 0 \)

Answer 16

we knw for sure that x and (x-6) can NOT have same signs

Answer 17

Right.

Answer 18

right ? that much is obvious eh

Answer 19

good :) we're left wid two cases

1) x positive, (x-6) negative
2) x negative, (x-6) positive

Answer 20

Got that

Answer 21

check each of them if they satisfy the inequality

Answer 22

1) x positive, (x-6) negative

\(x\ge 0\), \(x-6 \le 0\)
\(x\ge 0\), \(x \le 6\)

this is one solution set,
lets see if other case gives something

Answer 23

2) x negative, (x-6) positive
\(x \le 0 , x-6 \ge 0\)

\(x \le 0 , x \ge 6\)

NOT POSSIBLE for the x to be less than 0, and greater than 6, at the same time !

Answer 24

so, oly solutions are from case 1 above

Answer 25

You are awesome @ganeshie8
Can you help me put this in interval notation?

Answer 26

Since

Answer 27

from case 1, we have
\(x \ge 0 , x \le 6\)

\( 0 \le x \le 6\)

Answer 28

you wanto put it in interval notation ?

Answer 29

Right. I got this below:

Answer 30

below interval notation :-

[0, 6]

Answer 31

The brackets meaning equal to.

Answer 32

yup !!

Answer 33

GOD BLESS YOU!

Answer 34

lol, one small trick when doing these

Answer 35

u familiar wid parabolas ?
quadratic equations ?

Answer 36

\(x(x-6)\le0 \)

see that, left side is a quadratic, wid x intercepts at 0 and 6

Answer 37

absolutely.