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Simple Inequalities

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Intern
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Simple Inequalities [#permalink] New post 07 Nov 2005, 09:44
Friends,

Could anybody solve these basic questions. Sorry my maths is not too strong.

1. 6>x+4>4 2. 2x > x+10 > -x
3. x+2y=9 4. -x+1 <= 63 + x (x>= -31 or x <=-31)
2x-3y = 4.


And one simple ratio .

1. 1.6 : 0.4 : 0.16

Please explain your answers . In equalities and ratios when 3 terms are involved, i am confused.
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 [#permalink] New post 07 Nov 2005, 12:45
AlexT, I can try simplyfying these inequlities but do you mind formatting them?
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 [#permalink] New post 07 Nov 2005, 13:49
Moreover, there are only two variables and not 3...
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 [#permalink] New post 07 Nov 2005, 19:40
Ok. More simply i can write them as :

1. 6>x+4>4

2. 2x > x+10 > -x

3. -x+1 <= 63 + x (Answer should be x>= -31 or x <=-31)

4. x+2y=9
2x-3y = 4.


And one simple ratio .

1. 1.6 : 0.4 : 0.16

And i mean to say 3 TERMS and not 3 VARIABLES.

THANKS.
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 [#permalink] New post 07 Nov 2005, 22:47
1. 6>x+4>4
take each side of equality seprately
6>x+4 ==> x<2 and x+4>4 ==> x>0

so 0<x<2


2. 2x > x+10 > -x

2x>x+10 => x>10
x+10>-x => 2x>10 => x>5

so x>5 and x>10 which means x>10 which will statisfy x>5

3. -x+1 <= 63 + x (Answer should be x>= -31 or x <=-31)

first take <
-x+1<63 + x => 2x>-62 => x>-31
Now
-x +1 = 63 + x => 2x= -62 => x=-31

so
x>= -31



4. x+2y=9
2x-3y = 4.

multiply the first equation by 2 and subtract 2 from first ..this will get rid of x and gives the value of x y as 2 put this in first equation and y = 5.

didn't understand what you mean by solving the ratio..
  [#permalink] 07 Nov 2005, 22:47
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