If A and B are nonzero integers with the same signs is the product negative or postitive

1 answer:

3 0

Remember.

positive number x positive number = positive number
positive number x negative number = negative number
negative number x positive number = negative number
negative number x negative number = positive number

So if both numbers have the same sign, either both positive or both negative, then the product will be positive.

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$\large\boxed{b\geq3\to b\in[3,\ \infty)}$

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$2(b-3)\geq3(3-b)\qquad\text{use the distributive property:}\ a(b+c)=ab+ac\\\\(2)(b)+(2)(-3)\geq(3)(3)+(3)(-b)\\\\2b-6\geq9-3b\qquad\text{add 6 to both sides}\\\\2b-6+6\geq9+6-3b\\\\2b\geq15-3b\qquad\text{add}\ 3b\ \text{to both sides}\\\\2b+3b\geq15-3b+3b\\\\5b\geq15\qquad\text{divide both sides by 5}\\\\\dfrac{5b}{5}\geq\dfrac{15}{5}\\\\b\geq3$