Question

Can someone help me solve inequalities
|5-m| >or equal to 7

Can someone help explain this to me??

Answer 1

I can help explain

Answer 2

You understand absolute value and inequalities, right?

Answer 3

yes for example
|-2| =2 |3| = 3
no matter what its sign is right?

Answer 4

yes

Answer 5

so for every value in there, it must always be greater than 7

Answer 6

are you graphing this?

Answer 7

what do you mean by graphing?

Answer 8

Did they ask you to graph it, or is this the entire question

Answer 9

inequalites can be graphed

Answer 10

but i'll go ahead and show u how to solve it

Answer 11

so absolute values don't have a real opposite, like addition and subtraction for example

Answer 12

so you just ignore them really

Answer 13

Yeah they do

Answer 14

they do?
i think i'm having a brain fart here

Answer 15

one second

Answer 16

ok

Answer 17

Actually, thinking about this equation

Answer 18

every value for x < -2 and x > 12 works

Answer 19

so there's a break in the line, and I never remember doing that

Answer 20

They ask me to state the equation or inequality as a disjunction or conjuction then solve it and graph it

Answer 21

OH
i remember

Answer 22

its a disjunction

Answer 23

to solve it, you can use the +/- sign

Answer 24

solve for m - 5 and -m + 5

Answer 25

basically flipping the signs in the second one

Answer 26

solving for m - 5, it's m >/= 12
solving for -m + 5, it's
-m < 2
m = -2

Answer 27

made a typo, i meant m>/=-2

Answer 28

and when you flip the signs, always turn the inequality sign around

Answer 29

So to graph it

Answer 30

there are two lines drawn

Answer 31

one for -m + 5 < 7 and one for m - 5 > 7

Answer 32

the line will be a solid one, not dashed as it's a </= sign

Answer 33

okay give me a second im trying to grasp all of this

Answer 34

do i need to explain the graph?

Answer 35

Ok, ask if you need help

Answer 36

brb, need to submit a test i'm taking

Answer 37

few seconds

Answer 38

so for example FI have |5-m| >or equal to 7 FIRST I change that to
|5-m| >/ 7 AND |5-m| \< 7 correct?

Answer 39

Then wouldn't I have to add 5 to both sides??

Answer 40

back

Answer 41

oops wait hold on
I did that for the wrong inequality thats for less than

Answer 42

Ok, so m-5>= 7, and -m+5 =<7

Answer 43

Without it, it would be a regular inequality

Answer 44

I'll list the steps for solving both equations

Answer 45

For |m-5| >= 7:
|m| >= 12, but it should be written as m >= 12

Answer 46

what i did there is add 5 to both sides

Answer 47

For |-m+5| < 7:
|-m| < 2 (-5 both sides)
|m| < -2 (multiplied by -1)

Answer 48

i'm just going to delete the spam omments and explain it all in one mega-comment

Answer 49

im so confused @~@

Answer 50

yeah i'm sorry

Answer 51

Ok here goes

Answer 52

To solve an inequality with an absolute value sign, you must solve the original and inverted form of it

Answer 53

The original, in this case, is |m-5| >= 7

Answer 54

the inverted is multiplying the whole left side by -1

Answer 55

so |-m+5| <= 7 (and flipping the inequality sign)

Answer 56

Then, to make things simple, just take away the absolute value signs and solve for m

Answer 57

first why do yo you multiply it by -1 (sorry im just trying me best to undertand this step by step

Answer 58

because absolute values don't care about negatives

Answer 59

alright

Answer 60

if m was -2, it would solve to
|-2 -5| = 7
|-7| = 7

Answer 61

that's why

Answer 62

so solving the original, we get:
|m-5| >=7
|m| >= 12 (add 5 both sides)

Answer 63

and the inverted:
-m + 5 <= 7
-m=2 (subtract 5 both sides)
m=2(multiply by -1)

Answer 64

Now for graphing it

Answer 65

Because m >= 12 OR m<=-2, it is a disjunction

Answer 66

or = disjunction

Answer 67

What you do here is you remove the inequality sign for both the original and inverted equation, and replace them with a = sign

Answer 68

so you can have the lines for your graph
there are going to be two lines, you shade in a certain part of them

Answer 69

wait a minute, this is a 1-variable equation

Answer 70

you can only plot it on a number line

Answer 71

if they say to graph it, then somethings wrong

Answer 72

to graph this, just put points at -2 and 12 on a number line (make sure they are filled in dots because of the >= sign) and draw lines going outwards

Answer 73

and that's it

Answer 74

sorry for confusing you at first

Answer 75

let me check the paper again

Answer 76

ok

Answer 77

and don't worry about it
thats fine

Answer 78

if they say to graph it, they're wrong, just draw a number line and inform whoever gave it to you of their mistake

Answer 79

unless by graph they mean graph a number line which sounds weird

Answer 80

they don't really explain it they just say to graph it, don't worry about it I'll talk to them and explain but thank you anyway for helping with this question

Answer 81

ok, np
sorry for confusing you at first

Answer 82

tag me if you need help

Answer 83

I will, again thank you :)