Question

Need help for college algebra, desperate, find values for x so that the perimeter of the figure is less than 140 meters.

Length of rectangle x+4, width x

Answer 1

2(x+4) +2(x) < 140

Answer 2

the perimeter of a rectangle is 2 sides and 2 widths

Answer 3

2x + 8 + 2x < 140

Answer 4

4x < 132

Answer 5

x < 33

Answer 6

ok that makes a lot of sense now thank you. @DanJS do you happen to know interval notation too?

Answer 7

u understand all that?

Answer 8

sure ask away

Answer 9

wait about the last question would it be less than or equal to or just less that, if so why?

Answer 10

than*

Answer 11

it says in the question that the perimeter is less than

Answer 12

P < 140

Answer 13

ans P = 2(Length) +2(Width) for a rectangle

Answer 14

ok, sorry that was a dumb question. x<3, write in interval notation, I thought it would be (-infinity,) but I'm not sure.

Answer 15

(-infinity,3)*

Answer 16

right, if it is just "less than" you use a parenthesis
if it is also equal to, you would use a bra - ket

Answer 17

the only restriction is that x is less than 3

Answer 18

(-infinity , 3)

Answer 19

ok

Answer 20

How about x is greater than 3 but less than or equal to 63

Answer 21

(3,63]
?

Answer 22

correct, you got it

Answer 23

Can I ask one more question? I promise its the last, I'm just studying for an exam for monday.

Answer 24

no prob

Answer 25

Solve the inequality symbolically. The solution set is {t| }

Answer 26

\[\frac{ 5 }{ 4 }(6t-5) \le \frac{ 1 }{ 2 }(16t-7) + 3\]

Answer 27

I would multiply everything by 4 to begin with

Answer 28

\[5(6t-5) \le 2(16t-7) + 12\]

Answer 29

see that?

Answer 30

yes, so 30t-25≤32t-2

Answer 31

yes

Answer 32

-2t<=23

Answer 33

yes

Answer 34

t>=-11.5

Answer 35

yes! you switched the sign because you divided by a negative number.

Answer 36

so the interval is then?

Answer 37

so is the solution set just 11.5?

Answer 38

oh

Answer 39

{t such that t >=11.5}

the "such that" is the vertical line

Answer 40

or is the solution set also in interval notation?

Answer 41

no they wanted it in that notation, which reads "All t, such that t is greater than or equal to 11.5"

Answer 42

So when I get a problem on the test like this one would I just put -11.5 in the gap?

Answer 43

the vertical line is "such that"
the gap would be your inequality

Answer 44

so t >=-11.5

Answer 45

yeah, that is what that notation does, it states the variable "all t" vertical line "such that" then restrictions if any

Answer 46

if no restrictions, then

Answer 47

Ok, so just to be clear on interval notation, if I do -5<x<=6, it would be like (-5,6]

Answer 48

\[t \epsilon \mathbb{R} \]

Answer 49

t is an element of the real numbers, if there are no restrictions,

Answer 50

ok, that makes sense. Ok, so just to be clear on interval notation, if I do -5<x<=6, it would be like (-5,6]

Answer 51

yeah you are right

Answer 52

ok thank you, i really appreciate your help.

Answer 53

np, feel free to ask anytime, you are one of very few that actually want to understand and not just given answers. :)