# How do you solve #(x-4)(x+3)<0#?

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This inequality is saying that the product of two things is less than zero, or in other words, negative.

If the product of two things is negative, one of them has to be negative. So we can say

We can't have the same signs, because that would make the solution set positive.

Isolating the

These solutions overlap each other, as the only values of

Hope this helps!

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You have to consider two possibilities:

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For a product to be negative, one of the factors must be negative and the other positive.

(1)

This leads to:

(2)

This leads to:

These two contradict.

So the solution space is

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graph{(x-4)(x+3)<0 [-3.22, 4.576, -2.05, 1.85]}

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we have

these are the values on which the sign of the equation changes

to get a range for x mark these critical points on a real number line

take any value between -3 and 4 (lets say 0)

now take any value greater than 4 or less than -3

case 1(greater than 4)

similarly

case -2(less than -3)

hence the required solution

Describe your changes (optional) 200