anonymous
  • anonymous
Help for a medal, anyone? I'm rusty on inequalities and need some help on a few problems to boost my memory. Here's the first one... -9 < 4x + 8 < 10
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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amistre64
  • amistre64
what are your thoughts ...
anonymous
  • anonymous
If I remember correctly, you're supposed to simplify the equation by adding, divining..etc terms on either side, but I'm not sure how to do that with an inequality.
anonymous
  • anonymous
dividing*

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amistre64
  • amistre64
the math doesnt change ... what you do to one part, you do to all the parts to keep them "equal" right?
amistre64
  • amistre64
in this case, the equation is in the middle instead of to the left or right ... what would you think we should do first?
amistre64
  • amistre64
just make a guess at what you think we should do to start with ... what comes to mind? 4x+8 is what we want to manipulate, how do we work about getting 'x' all by itself?
anonymous
  • anonymous
Would you solve one equality at a time like -9 < 4x + 8 or 4x + 8 < 10 ?
amistre64
  • amistre64
you can if you want, but i just work it all at once to avoid the extra work of writing it all out twice
amistre64
  • amistre64
-9 < 4x + 8 < 10 -8 -8 -8 ---------------- -17< 4x < 2
anonymous
  • anonymous
Ah, I see. Then you would divide all 3 parts by 4 to get x by itself.
amistre64
  • amistre64
correct, the only thing to watch out for is when we have to mulitply or divide by a negative number ... which they really should include the rule when doing equalities the sign reverses ... but we do not have to worry about that in this particular case do we
amistre64
  • amistre64
if -a < b, then a > -b if -a > b, then a < -b if -a = b, then a = -b ... the reversing of an equals sign just produces an equals sign, but it helps to make the rule consistent for all 3 equality signs.
anonymous
  • anonymous
So would -17/4 < x < 1/2 be the final answer or is there another step?
amistre64
  • amistre64
thats the answer for me, but im not grading it
amistre64
  • amistre64
17/4 cant be reduced, but it can be written as 4 and 1/4 if need be
anonymous
  • anonymous
Okay, thank you. :) Could you help with one other? It looks a bit different from the first.
amistre64
  • amistre64
i spose
anonymous
  • anonymous
\[\left|\frac{ x+4 }{ 5 } \right| < 6\]
amistre64
  • amistre64
absolute value, what does that mean to you?
anonymous
  • anonymous
I know that nothing inside of it can be negative (or at least that I recall)
amistre64
  • amistre64
first off |5| = 5 so we can go ahead and multiply thru by 5 |x+4| < 30
amistre64
  • amistre64
it can be negative inside of it, but the bars cancel out the sign
amistre64
  • amistre64
|-30| = 30 and |30| = 30 when does x+4 = 30? or -30?
amistre64
  • amistre64
as a side note: |a| < k can be written as: -k < a < k
amistre64
  • amistre64
|x+4| < 30 can be written as -30 < x+4 < 30
anonymous
  • anonymous
Then you just subtract 4 from both sides... -34 < x < 26 Also does the |a| < k or -k < a < k rule always apply?
amistre64
  • amistre64
it is a rule, so it always applies yes. its just my brain that doesnt always remember it in time lol
amistre64
  • amistre64
\[|\frac{x+4}{5}|<6\] \[-6<\frac{x+4}{5}<6\] \[-306
amistre64
  • amistre64
not -306, but yeah
anonymous
  • anonymous
Oh, okay. So -34 < x < 26 would be the answer correct?
amistre64
  • amistre64
looks good to me
anonymous
  • anonymous
Thank you so much for your help. :)
amistre64
  • amistre64
youre welcome, and good luck :)

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