The product of three more than a number times two less than the number is fourteen. How do you find the number?

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Answer 1 · 2016-11-18T17:20:46

The number is either #-5# or #4#.

From the given data, we can write the equation:

#(x+3)xx(x-2)=14#

Opening the brackets and simplifying, we get:

#x^2+3x-2x-6=14#

#x^2+x-6=14#

Subtract #14# from each side.

#x^2+x-20=0#

Factorise.

#x^2+5x-4x-20=0#

#x(x+5)-4(x+5)=0#

#(x+5)(x-4)=0#

#x+5=0# or #x-4=0#

#x=-5# or #x=4#