The product of some negative number and 7 less than three times that number is 6. How do you find the number?

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Answer 1 · 2016-12-11T01:28:37

The number is $-3$ .

Let us consider the negative number as $-x$ . From the data, we can write:

$-x(-3x-7)=6$

Open the brackets.

$3x^2+7x=6$

Subtract $6$ from both sides.

$3x^2+7x-6=0$

Factorise.

$3x^2+9x-2x-6=0$

$3x(x+3)-2(x+3)=0$

$(3x-2)(x+3)=0$

$3x-2=0$ or $x+3=0$

$3x=2$ or $x=-3$

$x=2/3$ or $x=-3$

Applying the given data to the two possibilities, only the second possibility applies.

$:.x=-3$