help with algebra, 10 points!?

Question

2x-5=height
3(4+x)= length

if the perimeter of the rectangle is less than 52, find all possible values for x.

Answer 1

the perimeter formula is 2lenth +2 width

so you set the problem up like so
2(2x-5)+2(3(4+x))<52
multiply it out
4x-10+24+6x<52
combine like terms
10x+14<52
10x<38
x<3.8
since x must be a positve number
0

Answer 2

The perimeter is the sum of two heights and two lengths. p=2h+2l

h=2x-5 and l=12+3x (distributing the 3, there)

Substitute the equations for h and l into the first equation for p:

p=2(2x-5)+2(12+3x)=4x-10+24+6x=10x+14

So, in terms of x, the perimeter is equal to 10x+14. And we know the perimeter is less than 52, so 10x+14 is less than 52. Or, more mathily: 10x+14<52, which can be reduced to:

5x+7<26

5x<19

x<19/5

Answer 3

Perimeter is 2l+2h, so:
2(2x-5) + 2[3(4+x) < 52
(4x-10) + 2(12+3x) < 52
(4x-10) + (24+6x) < 52
10x+14 < 52
10x < 38
x < 3.8
Since neither l nor h can = 0,
4x-10>0 and 6x+24>0
The only one that could be negative is
4x-10>0, so 4x>10 and x>10/4 (2.5)

Thus 2.5 < x < 3.8

Hope this helps, and hope i didn't misread the question.

Answer 4

2(2x - 5) + 2 [3(4+x)] < 52
4x - 10 + 2(12+3x) < 52
4x-10+24+6x < 52
10x+14 < 52
10x < 52 - 14
10x < 38
x < 3.8
Since there's no negative measurement, it is between 0 and 3.8

0

Answer 5

At the extreme, 2h+2l=52. This is 4x-10 + 24+6x.
Combining terms 10 x + 14 =52 and 10x=38.
So x < 3.8 ft.

Answer 6

2x-5= height
3(4+x)= length

2[(2x - 5) + 3(4 + x)] < 52
4x - 10 + 24 + 6x < 52
10x + 14 < 52
10x < 38
x < 3.8

Therefore, all possible values for x are in range:

0 < x < 3.8
x = 1,2, or 3

Answer 7

2x-5=height
3(4+x)=lenght
(I can't put the" less than" symbol)

(2x-5)+3(4+x) <52
2x-5+12+3x <52
2x+3x-5+12 <52
5x+7 < 52
5x <52-7
x < 45/5
x < 9

So, the ans is x less than 9

Answer 8

2h +2l = 4x-10 + 24+6x = 10x + 14 <52

therefore 38<10x ----> 3.8

Answer 9

m

Answer 10

1,2,3,4,5,6,7,8,9,10,11