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

Answer 1

Abigail Allen

The number is #-3#.

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

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

Slide the brackets open.

#3x^2+7x=6#

Subtract #6# from both sides.

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

Factorize.

#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#

When the provided data is applied to the two possibilities, only the second one is viable.

#:.x=-3#

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Answer 2

Julia Adams

Let the negative number be ( x ).

According to the given information, the equation representing the problem is: ( x(3x - 7) = 6 ).

Solve the equation for ( x ) to find the number.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.