# Inequalities

#### Monkeyseat

##### Full Member
This is the question (in 2 parts really).

Part 1: A rectangular plot of land has dimensions 2x + 3 meters by 5x - 4 meters. Explain why x > 4/5.

Part 2: Given that the perimeter is less than 40 meters, find another inequality satisfied by x.
This is what I did:

Part 1:

2x + 3 > 0

This has to be bigger than 0 in length.

2x > -3

x > -3/2 or -1.5

It cannot be this low i.e. x cannot be a negative length like -1.4.

-----------

5x - 4 > 0

This has to be bigger than 0 in length.

5x > 4

x > 4/5 or 0.8

This length satisifies both sides so it must be this. It is greater than 0.

-----------

Part 2:

2 (2x + 3) + 2 (5x - 4) < 40

4x + 6 + 10x - 8 < 40

14x - 2 < 40

14x < 42

x < 3
I think I have kinda done it right (well at least part 2) but am I right with the first part of the question - the bit about 4/5?

It's just I looked at the answers in the back of the book and they only used the bit 5x - 4 > 0 to prove that x > 4/5 so am I right that is why they didn't use 2x + 3 > 0 because it can't be a negative length? I mean that x > -3/2 or -1.5 can't be true?

Baisically, can someone clear up (the first part of the question) why they are asking to prove that x is 4/5 and not use 2x + 3 > 0 and get -3/2 or -1.5? Is it because of the negative sign? I.E. you can't have -1.5cm?

The book's answer to this was:

5x - 4 > 0 (can't have a negative length), therefore 5x > 4, therefore x > 4/5 then x < 3.
Sorry if that was a bit messy/didn't make sense. I tried to make it as uncomplicated as possible.

Many thanks.

#### stapel

##### Super Moderator
Staff member
Far from being at all "messy", your work looks great to me! :wink:

Eliz.

#### Monkeyseat

##### Full Member
Thanks.

So was I right about the first part, it can't be a negative so it's 4/5 and not -3/2?

#### Subhotosh Khan

##### Super Moderator
Staff member
Monkeyseat said:
Thanks.

So was I right about the first part, it can't be a negative so it's 4/5 and not -3/2?
From the first part, you get

x > - 1.5....................................................(1)

From the first part, you get

x > 4/5....................................................(2)

(2) includes (1) - that is whenever x > 4/5 it is also greater than -1.5 (for example 1 > 4/5 and also 1>-1.5

However, (1) does not include (2) [ for example -1 > 1.5 but -1<4/5]

So When you have to satisfy (1) and (2) - you can state only (2).

#### Monkeyseat

##### Full Member
Subhotosh Khan said:
Monkeyseat said:
Thanks.

So was I right about the first part, it can't be a negative so it's 4/5 and not -3/2?
From the first part, you get

x > - 1.5....................................................(1)

From the first part, you get

x > 4/5....................................................(2)

(2) includes (1) - that is whenever x > 4/5 it is also greater than -1.5 (for example 1 > 4/5 and also 1>-1.5

However, (1) does not include (2) [ for example -1 > 1.5 but -1<4/5]

So When you have to satisfy (1) and (2) - you can state only (2).
Ok thank you I understand that, but did you make a typo i.e. you said "-1 > 1.5" did you mean "-1 > -1.5"?

Also was I right when I said x could not be -3/2 anyway as you cannot have -3/2 m??? -1.5m does not exist right?

Thank you.

EDIT:

I think I understand now, x can be less than 0 as x alone is not the length of the side. 2x + 3 is the length of the side. As long as that is bigger than 0 x can be less (although it won't satisfy both sides in this case). Is that right?

So really my reasoning in the first question was wrong when I said:

"It cannot be this low i.e. x cannot be a negative length like -1.4"

"This length satisifies both sides so it must be this. It is greater than 0."

I just judged it on the fact that x was bigger than or less than 0 when that wasn't what should be done - it should be the whole thing i.e. 2x + 3. I thought I checked though with both numbers and they both satisfied it so I must have made an error that's why I came up with that explanation.

I think you must have meant stapel that the whole thing has to be bigger than 0 (?), not x like I was thinking so I apologise.

Anyway, I've removed that bit and amended my work. Please can someone just check the bits I mentioned.

I'll try check back soon (ASAP) when I get a free minute.

Cheers.

EDIT EDIT:

Oh and forgot to say in my other post, thanks to whoever edited the pic to text. I thought it was ok though... :?: Anyway sorry if it's no pics, I just thought it was easier to take a screenshot and it would be formatted clearer.

#### stapel

##### Super Moderator
Staff member
Monkeyseat said:
...thanks to whoever edited the pic to text.
Pictures are fine, and sometimes crucial. But when the exercise is just text anyway, then (since temporarily-needed pictures tend to disappear after a while) a screen-shot of text may be replaced with the actual text. In this way, the "conversation" is preserved in better condition for future students' use.

Thank you!

Eliz.

#### Monkeyseat

##### Full Member
So was my resoning correct in my previous post?

Cheers.

#### Monkeyseat

##### Full Member
Just to bring this back up, if someone can clarify whether my above answer (the post starting "Ok thank you I understand that" ironically lol) is right or wrong that would be great. Sorry for asking so many questions (or being a hassle); it's just this last one.

Thank you.