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3(3x+2)<8(x+2)<6(5x-12) =


Sagot :

Pepe11idn
3(3x+2) < 8x + 16 => x < 10 
8x + 16 < 30x - 72  => 22x > 88 => x > 4
solution is  4  < x < 10
 
[tex]3(3x+2) < 8(x+2) < 6(5x-12)\\\\9x+6 < 8x+16 < 30x-72\\\\\#1\\9x+6 < 8x+16\ \ \ \ \ |subtract\ 6\ from\ both\ sides\\9x < 8x+10\ \ \ \ \ \ \ |subtract\ 8x\ from\ both\ sides\\x < 10\\\\\#2\\8x+16< 30x-72\ \ \ \ \ \ \ \ |subtract\ 16\ from\ both\ sides\\8x < 30x-88\ \ \ \ \ \ \ \ \ |subtract\ 30x\ from\ both\ sides\\-22x < -88\\22x > 88\ \ \ \ \ \ \ \ \ |divide\ both\ sides\ by\ 22\\x > 4\\\\From\ \#1\ \cap\ \#2\ we\ have\ 4 < x < 10\Rightarrow x\in(4;\ 10)[/tex]
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