Question 1071938
let x be the negative number.


-(13 + 1/2) is equal to -27/2


you get:


x + 1/4 * x + 7/16 * x = -27/2


multiply both sides of this equation by 16 to get:


16x + 4x + 7x = (-27 * 16) / 2


combine like terms to get:


27x = (-27 * 16) / 2


divide both sides of this equation by 27 to get:


x = (-27 * 16) / (2 * 27)


the 27 in the numerator and denominator cancel out and you are left with:


x = -16/2


solve for x to get:


x = -8


that should be your number.


to confirm, replace x in your original equation with -8 to get:


x + 1/4 * x + 7/16 * x = -27/2 becomes:


-8 -8/4 - (7*8)/16) = -27/2.


simplify to get:


-8 - 2 - 7/2 = -27/2


multiply both sides of this equation by 2 to get:


-16 - 4 - 7 = -27


combine like terms to get:


-27 = -27


this confirms the solution is correct.


your solution is that the negative number you are looking for is equal to -8.