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#