You can put this solution on YOUR website! 3x less than 2x - 3 or 7x greather than 4x - 9
3x<2x-3 ----(1)
-2x+3x <-2x+(2x-3)
[adding -2x to both the sides of the inequality(from the left)]
x<(-2x+2x)-3 (using additive associativity on the RHS)
x<0-3 (using additive inverse law)
x<(-3) ----(I)
7x> 4x-9
-4x+7x>-4x+(4x-9)
[adding -4x to both the sides of the inequality(from the left)]
3x> (-4x+4x)-9 (using additive associativity on the RHS)
3x>0-9
3x>-9
x>(-9/3) (division by a positive quantity does not alter the inequality)
That is x>(-3) ----(II)
Therefore 3x less than 2x - 3 or 7x greather than 4x - 9 means
either x<(-3) OR x>(-3)
Note: x CANNOT BE LESS THAN AND GREATER THAN (-3) simultaneously of course
(in the same given problem.)
Note: Only if the above problem is asked as an independent and individual problem you are to give all these elaborate steps.Otherwise you may simply transfer terms from one side to another taking care to change the sign while doing so and grouping like terms(along with the signs of course) for adding which is actually additive commutativity and associativity.
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