Solve each inequality. Then graph the solution set on a number line. Help me pls! M-8>-12

- anonymous

Solve each inequality. Then graph the solution set on a number line. Help me pls! M-8>-12

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- jim_thompson5910

how would you solve for M

- anonymous

I dont have an idea

- jim_thompson5910

we want to move that -8 over
so what can we do to both sides to do that?

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## More answers

- anonymous

Put the 8 on both sides?

- jim_thompson5910

subtract 8 from both sides?
or
add 8 to both sides?

- anonymous

Subtract?

- jim_thompson5910

-8 minus 8 = -16
but notice how -8 + 8 = 0

- jim_thompson5910

so this means you must add 8 to both sides

- anonymous

Wait im trying to gigure it out

- jim_thompson5910

sorry

- jim_thompson5910

just saw that message

- anonymous

Can you msg it again I'm little confused about it

- jim_thompson5910

M-8>-12
M-8+8 > -12+8 ... Add 8 to both sides.
M + 0 > -4
M > -4
hopefully all that makes sense

- jim_thompson5910

again, the reason why we add 8 to both sides is because -8+8 = 0 and that will go away on the left side

- anonymous

12+8?

- jim_thompson5910

it's -12+8

- anonymous

Oh yeah sorry didnt see negative sign

- jim_thompson5910

that's ok

- anonymous

I get it thanks but how about the graph solution

- jim_thompson5910

to graph M > -4 you
step 1) draw out a number line
step 2) plot an open circle at -4 (it's open because there isn't a line under the > sign)
step 3) shade to the right of the open circle
you shade to the right because of the greater than sign

- anonymous

I dont get it can you draw?

- jim_thompson5910

which step doesn't make sense

- anonymous

Okay nevermind. 6r<-36 my answer is r<-30 am i right?

- jim_thompson5910

6r means 6 times r

- jim_thompson5910

how do you undo multiplication?

- anonymous

Idk

- anonymous

Why r is times? I dont get it

- jim_thompson5910

that's what 6r means, it means 6 times r

- anonymous

So its 0

- anonymous

Then -36^6

- jim_thompson5910

what operation is the opposite of multiplication

- anonymous

Divide so i get -6

- anonymous

R>-6?

- jim_thompson5910

why did you flip the sign

- jim_thompson5910

the inequality sign

- anonymous

Oh yeah didnt see it

- anonymous

What if the case is like this -w denominator is 4 <_ cant insert it -7

- jim_thompson5910

what undoes division?

- anonymous

Multiplication?

- jim_thompson5910

good, so you multiply both sides by -4

- anonymous

Did you get my question?

- jim_thompson5910

yes you have to multiply both sides by -4

- anonymous

I got 16 and 28 what is next?

- jim_thompson5910

-1/4 times -4 is not 16

- anonymous

How to use that 1/4 inncalculator?

- jim_thompson5910

what is 1/4 in decimal form

- anonymous

.25

- jim_thompson5910

multiply that by 4

- anonymous

-16?

- anonymous

Its 16

- jim_thompson5910

0.25 times 4 = ??

- anonymous

1 or -1

- jim_thompson5910

it's 1

- anonymous

Then

- jim_thompson5910

this means -w/4 <= -7 turns into 1w >= 28

- jim_thompson5910

so the final answer is \[\large w \ge 28\]

- anonymous

Ohh you can cancel the one

- anonymous

Why the inequality signed change?

- jim_thompson5910

when you multiply both sides by a negative number, the inequality sign flips

- anonymous

Just multiply?

- jim_thompson5910

and divide

- anonymous

Oh tnx

- anonymous

I really suck at math :(

- jim_thompson5910

that's ok, just keep at it and you'll get better

- anonymous

4x-15<_21 what does it mean if the inquality sign has sign at the bottom?

- jim_thompson5910

it means that there's an "or equal to" part to it

- anonymous

So see ifnim right ill mltiply the 4 and the x and ill put the 4 on both sides

- jim_thompson5910

first you add 15 to both sides (to undo the -15)
then you divide both sides by 4 (to undo the 4 times x)

- anonymous

Ill put 15 and 4 to 21? -.-

- anonymous

Cancel the 15

- jim_thompson5910

\[\large 4x - 15 \le 21\]
\[\large 4x - 15+15 \le 21+15\]
\[\large 4x + 0 \le 36\]
\[\large 4x \le 36\]
\[\large \frac{4x}{4} \le \frac{36}{4}\]
\[\large \frac{1x}{1} \le \frac{36}{4}\]
\[\large 1x \le \frac{36}{4}\]
\[\large x \le \frac{36}{4}\]
\[\large x \le 9\]

- anonymous

Woah every setting change you really need to memorize it

- anonymous

Thanks i learned a lot from you ijust have one question on this number

- anonymous

-16>_5(2z-11) ill times the 5 to the 2 and 11 right do i still need to bring down the 5 after I times it?

- jim_thompson5910

\[\large -16 \ge 5(2z-11)\]
\[\large -16 \ge 5*2z-5*11\]
\[\large -16 \ge 10z-55\]
I'll let you finish

- anonymous

Thats what i did yeah

- anonymous

Z>29 am i right?

- jim_thompson5910

no that's incorrect

- anonymous

-61 or -144

- jim_thompson5910

first you add 55 to both sides

- anonymous

Why and then

- jim_thompson5910

what do you get when you add 55 to both sides

- anonymous

-7.1

- jim_thompson5910

no

- anonymous

Aw i really dnt know

- jim_thompson5910

\[\large -16 \ge 5(2z-11)\]
\[\large -16 \ge 5*2z-5*11\]
\[\large -16 \ge 10z-55\]
\[\large -16+55 \ge 10z\]
\[\large 39 \ge 10z\]
I'll let you finish

- anonymous

Z>49

- jim_thompson5910

no

- jim_thompson5910

10z means 10 times z

- anonymous

So z<39

- jim_thompson5910

that's also incorrect

- anonymous

39>z

- jim_thompson5910

divide both sides by 10

- anonymous

Z<3.9

- jim_thompson5910

good

- anonymous

Finally what does this mean define a variable and write an inequalityfor each problem

- anonymous

Example the quotientof three times anumber and 4 is at least -16

- jim_thompson5910

tell me what you got so far

- anonymous

What they mean by define a variable?

- jim_thompson5910

that just means pick a letter to represent the unknown number

- jim_thompson5910

usually x is chosen

- anonymous

Can you do these one for me coz i dnt have an idea and ill do the next one

- jim_thompson5910

ok this is the last one I'll help you with
"quotientof three times anumber and 4 is at least -16"
translates to
\[\large \frac{3x}{4} \ge -16\]

- jim_thompson5910

"quotientof three times anumber and 4 " means you'll have 3x over 4 as a fraction
and when you say "at least -16" it means "greater than or equal to -16"

- anonymous

Oh wait if the inequality has ni sign in the bittom i divided will switch

- anonymous

No

- anonymous

The quotient of the sum of 3 and a number and 6 is less than -2 my answer is 3x denominato 6 <_-2 am i right

- jim_thompson5910

it should be
\[\large \frac{3+x}{6} < -2\]

- jim_thompson5910

so you're somewhat close

- anonymous

Thank you so much for your help

- jim_thompson5910

you're welcome

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