Question

solve the inequality. graph your solution.
|x+3| > or equal to 15

Answer 1

Hint:

|x| > k

breaks into

x < -k or x > k

where k is some positive number

Answer 2

is it still correct if the arrows go in the same direction when I graph it?

Answer 3

no the arrows should be going in opposite directions

Answer 4

oh so you flip the sign when you make k a negative?

Answer 5

exactly

Answer 6

what did you get

Answer 7

x> or equal to 12 and x < or equal to -18

Answer 8

good, you got it

Answer 9

thanks :D

Answer 10

you're welcome

Answer 11

find the slope of the line passing through the given points. then tell whether the line rises, falls, is horizontal, or is vertical.

(-7,4) (5,-3)

Answer 12

use the slope formula

m = (y2 - y1)/(x2 - x1)

Answer 13

in this case

(x1,y1) = (-7,4)

(x2,y2) = (5,-3)

Answer 14

how do I find out whether the line rises, falls..etc ?

Answer 15

what did you get for the slope

Answer 16

-7/12

Answer 17

oh so the line decreases bc it has a negative slope?

Answer 18

you nailed it

Answer 19

Do you mind if i ask you questions from time to time ? I'm trying to study for a trig final on monday.

Answer 20

sure I can help

Answer 21

thanks! alright so this question has the same guidelines as the one we just did but with these coordinates (-5/4, 3); (2/3, 3) my friend had an error in her calculator trying to find the slope , but I got m=0 ...im confused

Answer 22

you're correct, it's 0

how do I know so quickly?

notice that the y coordinates are both equal to 3

since the y coordinates are equal, the slope will always be 0 because you have a horizontal line through y = 3

Answer 23

all horizontal lines have a slope of 0

Answer 24

using m = (y2 - y1)/(x2 - x1) we get

m = (y2 - y1)/(x2 - x1)

m = (3 - 3)/(2/3 - (-5/4))

m = 0/(2/3 - (-5/4))

m = 0

Answer 25

oh ok i understand

Answer 26

what if the x coordinates are equal? would that make the line vertical?

Answer 27

exactly

Answer 28

and the slope would be undefined

Answer 29

oh okay

Answer 30

how would i graph y=|x-3|?

Answer 31

do you know how to graph y = | x |

Answer 32

i think so? would there be 2 lines?

Answer 33

yes here is your blank xy axis

Answer 34

the graph of y = | x | looks like this

Answer 35

to graph y=|x-3|, you just shift over y = |x| three units to the right

Answer 36

im not sure i get you there...

Answer 37

imagine you can pick up that v shaped graph and move it around

well just move it over 3 to the right units like this

Answer 38

but how do i know the coordinates to create the v shape

Answer 39

i understand the moving it to the right part

Answer 40

the sharp point on the V of y = |x| is at (0,0)

move that point over 3 units to the right to get (3,0)

Answer 41

yes i understand that but what are the other coordinates for that shape?

Answer 42

for (3,0)..

Answer 43

(1,1) is on the original graph y = |x|

move that 3 units to the right to get (4,1)