#### Monkeyseat

##### Full Member

- Joined
- Jul 3, 2005

- Messages
- 298

This is what I did: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.

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?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.

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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.

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Part 2:

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

4x + 6 + 10x - 8 < 40

14x - 2 < 40

14x < 42

x < 3

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:

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

Many thanks.