Finding x for Real Number Complex Number z = (x+5) - (8-2x)i

To find the value of x such that z is a real number, we need to find when the imaginary part of z is equal to zero.

The imaginary part of z is given by (x+5) - (8-2x)i.

Setting this equal to zero, we have:

(x+5) - (8-2x)i = 0

Expanding this equation, we get:

x + 5 - 8 + 2xi = 0

Combining like terms, we have:

3 + 2xi = 0

Setting the real part equal to zero, we have:

3 = 0

This equation is not satisfied for any value of x.

Therefore, there is no value of x such that z is a real number.