Question

Why does the equation 35-5x+6x-36=-24-17x+17x+24 have one solution

Answer 1

Combining like terms first

x-1=0

x=1

It has only one solution because only one value of x satisfies the equation.

Answer 2

If it has only one solution that means that there is only one value of x that will fulfill this equation
35 - 5x + 6x - 36 = -24 - 17x + 17x + 24
-5x + 6x - 36 = -24 -17x + 17x + 24 - 35
x - 36 = -24 + 24 - 35 (I just canceled out the 17x because it would have justy made the process longer if I moved them over)
x = -24 + 24 - 35 + 36
x = -35 + 36
x = 1