Find the Value of x for a Real Number z: Complex Number Equation

To find the value of x such that z is a real number, we need to find the imaginary part of z, which is the coefficient of i, and set it equal to zero.\n\nThe imaginary part of z is given by (x+5) - (8-2x)i.\n\nSetting this equal to zero, we have (x+5) - (8-2x)i = 0.\n\nExpanding this equation, we get x + 5 - 8 + 2x = 0.\n\nCombining like terms, we have 3x - 3 = 0.\n\nAdding 3 to both sides of the equation, we get 3x = 3.\n\nDividing both sides by 3, we find x = 1.\n\nTherefore, the value of x such that z is a real number is x = 1.