Question

0

Answer 1

`The length of a rectangle is 2 ft more than four times the width` means L = 4W+2

`perimeter is less than 34 ft ` means P < 34


P < 34
2L+2W < 34
2(4W+2)+2W < 34
8W+4+2W < 34
10W+4 < 34
10W+4-4 < 34-4
10W < 30
10W/10 < 30/10
W < 3


If W is an integer, then the highest W can be is 2. The value of W cannot be 3 since W < 3


So you have the correct answer. Nice job

Answer 2

`do you know much about set builder notation?` yes I do

Answer 3

`Solve and write the solution in set-builder notation. 3x-1>2x+2`
`And I said that x>3 and {x|x>3}`

{x|x>3} is the correct way to write x > 3 in set builder notation

Answer 4

`Solve and write the solution in set-builder notation 3x+1<=7x-15`
`x>=4`
`{x|x>=4}`

also correct

Answer 5

`And the final one, -5<3x+4<16`
`And my answer was -3<x<4`
`{x|-3<x<4}`

also correct

Answer 6

yes. You did great

Answer 7

interval notation and set builder notation are slightly different. They represent the same idea though

Answer 8

for example, we can say

3 < x < 10

or we can write

(3,10)

the `(3,10)` in interval notation means start at 3 and end at 10. Exclude 3 from the interval. Exclude 10 from the interval

Answer 9

another example

2 < x <= 7

is written as

(2,7]

notice the use of a square bracket

the `(2,7]` in interval notation means start at 2 and end at 7. Exclude 2 from the interval. Include 7 in the interval

Answer 10

] means include the endpoint
) means exclude the endpoint

Answer 11

if you want to write something like x > 5, then you'd write (5, infinity)
if you want to write something like x >= 5, then you'd write [5, infinity)


if you want to write something like x < 5, then you'd write (-infinity, 5)
if you want to write something like x <= 5, then you'd write (-infinity, 5]


never use square brackets for infinity. You never can include infinity since it goes on forever

Answer 12

when you wrote `3/5x-2<3/10-x` did you mean to write \[\Large \frac{3}{5}x-2 < \frac{3}{10}-x\] or no?

Answer 13

`x<23/16`
`(-infinity, 23/16)`
are both correct

Answer 14

I'm glad it makes more sense now