If you multiply four negative numbers, what is the sign of the product? if you multiply five negative numbers, what is the sign of the product? based on the answers to these questions and the product rules, write a general rule for the sign of the product based on the number of negative numbers in the expression.

4 negatives:

(1)negative x (2)negative = positive x (3)negative = negative x (4)negative = positive

5 negatives:

(1)negative x (2)negative = positive x (3)negative = negative x (4)negative = positive x (5) negative = negative

 even number of negatives would equal a positive answer

odd number of negatives would equal a negative answer

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4