Question 64686
QUESTION:


solve the inequality.  


3(2-3x)+3x+5<-4(X-2)-2(x-3)-3



ANSWER:


3(2-3x) + 3x + 5 < -4(X-2) - 2(x-3) -3



Now remove parenthesis by multiplying them,


==> 3*2 - 3*3x  + 3x + 5 < -4X + 4*2 - 2*x + 2*3 -3


==> 6 - 9x + 3x + 5 < - 4x + 8 - 2x + 6 -3


==> 6 + 5 - 9x + 3x < -4x - 2x + 8 + 6 - 3


==> 11 - 6x < - 6x + 11


You cannot solve this expression any more.

Because such an inequality is not possible.
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If your question is like this,(ignoring negative sign of 4 )


3(2-3x) + 3x + 5 < 4(X-2) - 2(x-3) -3, 

Proceed as above.  Then we have,


Now remove parenthesis by multiplying them,


==> 3*2 - 3*3x  + 3x + 5 < 4X - 4*2 - 2*x + 2*3 -3


==> 6 - 9x + 3x + 5 <  4x - 8 - 2x + 6 -3


==> 6 + 5 - 9x + 3x < 4x - 2x - 8 + 6 - 3


==> 11 - 6x < 2x - 5


Now collect like terms together,


==> 11 + 5 < 2x + 6x


==> 16 < 8x


Divide both sides by 8


==> 16/8 < 8x/8



==> 2 < x


That is solution is x > 2.


If the inequality given in your question 

is 'less than or equal to'( that is <= ), 

Then soltuon becomes,  x greater than or equal to 2 (that is  x>= 2)



Check your question once again  and if it is wrong, submit correct question once again.








Hope you understood.


Regards.


Praseena.