anonymous
  • anonymous
Solve each inequality. Then graph the solution set on a number line. Help me pls! M-8>-12
Algebra
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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jim_thompson5910
  • jim_thompson5910
how would you solve for M
anonymous
  • anonymous
I dont have an idea
jim_thompson5910
  • jim_thompson5910
we want to move that -8 over so what can we do to both sides to do that?

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anonymous
  • anonymous
Put the 8 on both sides?
jim_thompson5910
  • jim_thompson5910
subtract 8 from both sides? or add 8 to both sides?
anonymous
  • anonymous
Subtract?
jim_thompson5910
  • jim_thompson5910
-8 minus 8 = -16 but notice how -8 + 8 = 0
jim_thompson5910
  • jim_thompson5910
so this means you must add 8 to both sides
anonymous
  • anonymous
Wait im trying to gigure it out
jim_thompson5910
  • jim_thompson5910
sorry
jim_thompson5910
  • jim_thompson5910
just saw that message
anonymous
  • anonymous
Can you msg it again I'm little confused about it
jim_thompson5910
  • 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
  • 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
  • anonymous
12+8?
jim_thompson5910
  • jim_thompson5910
it's -12+8
anonymous
  • anonymous
Oh yeah sorry didnt see negative sign
jim_thompson5910
  • jim_thompson5910
that's ok
anonymous
  • anonymous
I get it thanks but how about the graph solution
jim_thompson5910
  • 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
  • anonymous
I dont get it can you draw?
jim_thompson5910
  • jim_thompson5910
which step doesn't make sense
anonymous
  • anonymous
Okay nevermind. 6r<-36 my answer is r<-30 am i right?
jim_thompson5910
  • jim_thompson5910
6r means 6 times r
jim_thompson5910
  • jim_thompson5910
how do you undo multiplication?
anonymous
  • anonymous
Idk
anonymous
  • anonymous
Why r is times? I dont get it
jim_thompson5910
  • jim_thompson5910
that's what 6r means, it means 6 times r
anonymous
  • anonymous
So its 0
anonymous
  • anonymous
Then -36^6
jim_thompson5910
  • jim_thompson5910
what operation is the opposite of multiplication
anonymous
  • anonymous
Divide so i get -6
anonymous
  • anonymous
R>-6?
jim_thompson5910
  • jim_thompson5910
why did you flip the sign
jim_thompson5910
  • jim_thompson5910
the inequality sign
anonymous
  • anonymous
Oh yeah didnt see it
anonymous
  • anonymous
What if the case is like this -w denominator is 4 <_ cant insert it -7
jim_thompson5910
  • jim_thompson5910
what undoes division?
anonymous
  • anonymous
Multiplication?
jim_thompson5910
  • jim_thompson5910
good, so you multiply both sides by -4
anonymous
  • anonymous
Did you get my question?
jim_thompson5910
  • jim_thompson5910
yes you have to multiply both sides by -4
anonymous
  • anonymous
I got 16 and 28 what is next?
jim_thompson5910
  • jim_thompson5910
-1/4 times -4 is not 16
anonymous
  • anonymous
How to use that 1/4 inncalculator?
jim_thompson5910
  • jim_thompson5910
what is 1/4 in decimal form
anonymous
  • anonymous
.25
jim_thompson5910
  • jim_thompson5910
multiply that by 4
anonymous
  • anonymous
-16?
anonymous
  • anonymous
Its 16
jim_thompson5910
  • jim_thompson5910
0.25 times 4 = ??
anonymous
  • anonymous
1 or -1
jim_thompson5910
  • jim_thompson5910
it's 1
anonymous
  • anonymous
Then
jim_thompson5910
  • jim_thompson5910
this means -w/4 <= -7 turns into 1w >= 28
jim_thompson5910
  • jim_thompson5910
so the final answer is \[\large w \ge 28\]
anonymous
  • anonymous
Ohh you can cancel the one
anonymous
  • anonymous
Why the inequality signed change?
jim_thompson5910
  • jim_thompson5910
when you multiply both sides by a negative number, the inequality sign flips
anonymous
  • anonymous
Just multiply?
jim_thompson5910
  • jim_thompson5910
and divide
anonymous
  • anonymous
Oh tnx
anonymous
  • anonymous
I really suck at math :(
jim_thompson5910
  • jim_thompson5910
that's ok, just keep at it and you'll get better
anonymous
  • anonymous
4x-15<_21 what does it mean if the inquality sign has sign at the bottom?
jim_thompson5910
  • jim_thompson5910
it means that there's an "or equal to" part to it
anonymous
  • anonymous
So see ifnim right ill mltiply the 4 and the x and ill put the 4 on both sides
jim_thompson5910
  • 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
  • anonymous
Ill put 15 and 4 to 21? -.-
anonymous
  • anonymous
Cancel the 15
jim_thompson5910
  • 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
  • anonymous
Woah every setting change you really need to memorize it
anonymous
  • anonymous
Thanks i learned a lot from you ijust have one question on this number
anonymous
  • 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
  • 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
  • anonymous
Thats what i did yeah
anonymous
  • anonymous
Z>29 am i right?
jim_thompson5910
  • jim_thompson5910
no that's incorrect
anonymous
  • anonymous
-61 or -144
jim_thompson5910
  • jim_thompson5910
first you add 55 to both sides
anonymous
  • anonymous
Why and then
jim_thompson5910
  • jim_thompson5910
what do you get when you add 55 to both sides
anonymous
  • anonymous
-7.1
jim_thompson5910
  • jim_thompson5910
no
anonymous
  • anonymous
Aw i really dnt know
jim_thompson5910
  • 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
  • anonymous
Z>49
jim_thompson5910
  • jim_thompson5910
no
jim_thompson5910
  • jim_thompson5910
10z means 10 times z
anonymous
  • anonymous
So z<39
jim_thompson5910
  • jim_thompson5910
that's also incorrect
anonymous
  • anonymous
39>z
jim_thompson5910
  • jim_thompson5910
divide both sides by 10
anonymous
  • anonymous
Z<3.9
jim_thompson5910
  • jim_thompson5910
good
anonymous
  • anonymous
Finally what does this mean define a variable and write an inequalityfor each problem
anonymous
  • anonymous
Example the quotientof three times anumber and 4 is at least -16
jim_thompson5910
  • jim_thompson5910
tell me what you got so far
anonymous
  • anonymous
What they mean by define a variable?
jim_thompson5910
  • jim_thompson5910
that just means pick a letter to represent the unknown number
jim_thompson5910
  • jim_thompson5910
usually x is chosen
anonymous
  • anonymous
Can you do these one for me coz i dnt have an idea and ill do the next one
jim_thompson5910
  • 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
  • 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
  • anonymous
Oh wait if the inequality has ni sign in the bittom i divided will switch
anonymous
  • anonymous
No
anonymous
  • 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
  • jim_thompson5910
it should be \[\large \frac{3+x}{6} < -2\]
jim_thompson5910
  • jim_thompson5910
so you're somewhat close
anonymous
  • anonymous
Thank you so much for your help
jim_thompson5910
  • jim_thompson5910
you're welcome

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