Question 513949
We need to write this problem out algebraically.  Let x be the number.  Then twice that number is 2x, and twice the number decreased by 39 can be written as:

{{{ 2x - 39 }}}

The sum of the number and two times the number would be 

{{{x + 2x}}}

The problem states that twice a number decreased by 39 equals five time the sum of the number and two times the number.  We can therefore write this equation algebraically as:

{{{ 2x - 39 = 5(x + 2x) }}}

Now we simplify our equation and solve for x:

{{{ 2x - 39 = 5(3x) }}} (combine like terms)
{{{ 2x - 39 = 15x }}} (simplify the right hand side by multiplying)
{{{ -39 = 13x }}} (subtract 2x from both sides)
{{{ -3 = x }}} (divide both sides by 13)

So x = -3.  Let's check this: twice of -3 is -6, so twice of 3 decreased by 39 equals -6 - 39 = -45.  The sum of -3 and twice of -3 is -3 + (-6) = -9, and five times that is -45.  So the two sides match, and x = -3 is our solution.