Can we do this with greater than sign

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The discussion revolves around solving the inequality (2x-9)(x+3)≥0 and whether it is valid to separate the factors into (2x-9)≥0 and (x+3)≥0. Participants confirm that it is permissible to analyze the factors separately, as the product is non-negative when both factors are either positive or negative. There is a consideration of whether both factors can be negative simultaneously. Overall, the conversation emphasizes the validity of separating the inequalities for solving the problem.
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Can we do this with "greater than" sign

If (2x-9)(x+3)\geq0 then can we say (2x-9)\geq0 and (x+3)\geq0 and solve them seperately ? I am not sure if i can do this because of the \geq sign.

Hmm wrong section. Actually this is part of my homework anyway. :biggrin:
 
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Yeah you can do that because you are dividing both sides by the binomials and 0/ by anything equals 0.
 
The product will also be positive if both factors are negative.
 
If (2x-9)(x+3)\geq0 then can we say (2x-9)\geq0 and (x+3)\geq0 and solve them seperately ? I am not sure if i can do this because of the sign.
this is part of the solution only...
Hints
could both values inside the bracket be negative?
 
Thx a lot all and thanks again for the hint.
 
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