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Solve each of the inequality (x − 1)(x + 2) < 0 justifying each step by referring to an appropriate property or axiom of real numbers.​

Sagot :

The solution for the inequality (x − 1)(x + 2) < 0 if x-1 < 0  and x+2 > 0 and x ∈ (-2, 1)

What is inequality?

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

We have:

(x -1)(x + 2) < 0

The product of (x-1) and (x+2) is less than zero it means:

x-1 < 0  and x+2 > 0    or

x-1 > 0  and x+2 < 0  

Solve for first case:

x-1 < 0  and x+2 > 0

x < 1  and  x > -2

x ∈ (-2, 1)

Solve for the second case:

x > 1  and x < -2  

There will be no intersection region, so no solution in this case.

Thus, the solution for the inequality (x − 1)(x + 2) < 0 if x-1 < 0  and x+2 > 0 and x ∈ (-2, 1)

Learn more about the inequality here:

brainly.com/question/19491153

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