Question

Can someone please help me with this question? I have no clue how to do it....
Graph the inequality 102c + 150m + 41 > 500

Answer 1

@jdoe0001 and @mathstudent55 could one of y'all please try to show me how to graph?

Answer 2

@jim_thompson5910 could you try to help me?

Answer 3

Is this the problem we did a few days ago? If so, then treat 'c' as 'x'. Also, treat 'm' as 'y'

so you'll have 102x + 150y + 41 > 500

Answer 4

to graph `102x + 150y + 41 > 500`

you'll first need to graph `102x + 150y + 41 = 500` to form the boundary line

Answer 5

No sir/ma'am I don't think it is,

Answer 6

@jim_thompson5910 I don't know how to find the x and y values that I need to graph the inequality...

Answer 7

what is the value of y when x = 0 ?

Answer 8

5? @jim_thompson5910

Answer 9

no

Answer 10

102x + 150y + 41 = 500

102*0 + 150y + 41 = 500 ... replace x with 0

150y + 41 = 500

now solve for y

Answer 11

would I add 150 and 41?

Answer 12

no, they are on opposite sides of the equal sign

Answer 13

you need to move the 41 over, so subtract 41 from both sides

Answer 14

oh ok

Answer 15

so before i subtract it would look like this...
150y + 41-41 = 500-41? or this 41-150y + 41 = 500-41

Answer 16

`150y + 41-41 = 500-41` is the correct way

Answer 17

ok,
150y=459
y=150?

Answer 18

to isolate y in `150y=459`, you need to divide both sides by 150

Answer 19

150y means 150 times y

division is used to undo the multiplication

Answer 20

so it would equal 3? y=3?

Answer 21

you should have 459/150 = 3.06

Answer 22

oh yes sir/ma'am

Answer 23

ok so if x = 0, then y = 3.06

this is one point on the line

you need one more point to graph the line

Answer 24

plug in x = 1 and solve for y

Answer 25

I thought that's what i just did?

Answer 26

no you plugged in x = 0

Answer 27

oh

Answer 28

so in this -- 102x + 150y + 41 = 500
I would turn 150y into 3.06? like this... 102x + 3.06+ 41 = 500

Answer 29

102x + 150y + 41 = 500

102*1 + 150y + 41 = 500 ... replace x with 1

102 + 150y + 41 = 500

now isolate y

Answer 30

would I subtract 41 to both sides?

Answer 31

why not combine like terms on the left side?

Answer 32

what do you mean?

Answer 33

like-- 150y + 41 = 500+102?

Answer 34

`102 + 150y + 41 = 500`

102 and 41 are like terms on the left side

you can combine them

Answer 35

so 150y+143=500?

Answer 36

yep, now you subtract 143 from both sides to undo the addition

Answer 37

so, 143-150y+143=500-143?
7y=357?

Answer 38

you do NOT say 150y-143 = 7y

150y and 143 are NOT like terms, we cannot combine them

Answer 39

leave 150y alone as is

Answer 40

ok, well then I'm not sure how to do it

Answer 41

your next step is that you have 150y = 357

now divide both sides by 150

Answer 42

357/150=2.38

Answer 43

good

Answer 44

so before we found (0,3.06) as one point

another point is (1,2.38)

Answer 45

plot the two points (0,3.06) and (1,2.38)

then draw a straight line through them

Answer 46

oh ok... thats it?

Answer 47

that will take care of the line `102x + 150y + 41 = 500`

let me know when you've graphed it

there's a few more steps after this

Answer 48

ok I'm done

Answer 49

now we must use a test point

(0,0) is the easiest since 0 is easy to work with

Answer 50

(0,0) means x = 0 and y = 0

let's plug them both in

102x + 150y + 41 > 500

102*0 + 150y + 41 > 500 ... replaced x with 0

102*0 + 150*0 + 41 > 500 ... replaced y with 0

0 + 0 + 41 > 500

41 > 500

Answer 51

now ask yourself this: is `41 > 500` a true inequality? or is it false?

Answer 52

false

Answer 53

since `41 > 500` is false, this means `102x + 150y + 41 > 500` is false when (x,y) = (0,0)

so you do NOT shade the region where (0,0) is located. You shade the region on the opposite side of the line

Answer 54

In this case, it means you shade above the line `102x + 150y + 41 = 500`

Answer 55

So this is how it would look?