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Solve inequality

  • Thread starter MrNeWBiE
  • Start date
  • #1
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Homework Statement



Solve the inequality and write your answer in interval form.

2x+1 <= 5- x < x-7


The Attempt at a Solution



fist part 2x+1 <= 5- x
-4 <= -x
4 >= x

second part

5- x < x-7
0<-12 ,,,,,,,,,, O,O how it's gone be like this ?

well if it's right how i can write it in interval form ?
 

Answers and Replies

  • #2
tiny-tim
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Hi MrNeWBiE :smile:

(have a ≤ :wink:)
fist part 2x+1 <= 5- x
-4 <= -x

5- x < x-7
0<-12
No, both these are wrong, for the same reason:

when you transfer -x across an = or ≤, you must multiply it by -1.
 
  • #3
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ohhhh i see it now ,,,

2x+1 ≤ 5- x

-4≤-3x

x≤4/3

5- x < x-7
-2x<-12 .....x>6

now they are right ?

yet i didn't understand you ,,,,,
 
  • #4
tiny-tim
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Yup! :biggrin:

(I just meant that when you move -x across, it becomes +x, as you've done)

And now express that it interval form (you may need to use ∞). :wink:
 
  • #5
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(-∞,4/3]U[4/3,6) right ,,, ? or it's to ∞ not 6 ...
 
  • #6
tiny-tim
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(-∞,4/3]U[4/3,6) right ,,, ?
That's just (-∞,6) :rolleyes:
or it's to ∞ not 6 ...
and that's (-∞,∞). :smile:
 
  • #7
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i know that ,,,

but our tacher keep asking for more details ,,,,

if i write like this " (-∞,6) " he will say where is the 4/3 and the same for the other ,,, >.<
 
  • #8
tiny-tim
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if i write like this " (-∞,6) " he will say where is the 4/3
Yes, and that's because (-∞,6) is wrong!

Go back to x≤4/3

.....x>6.
 
  • #9
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x>6 how it's gone be x≤4/3 ,,,

isn't 6>4/3 ,,,=p

how x > 6 then x≤4/3 ??
 
  • #10
tiny-tim
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x>6 how it's gone be x≤4/3 ,,,

isn't 6>4/3 ,,,=p

how x > 6 then x≤4/3 ??
Exactly!

So that means … ? :smile:
 
  • #11
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no answers maybe ...
 
  • #12
tiny-tim
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Looks like it! :smile:
 
  • #13
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thx xD

sorry for wasting your time
 

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