1/2(4x-9)=2x+8
a.
exactly one real solution,

b.
no real solutions
c.
infinite real solutions

d.
exactly one real solution,

Let us first try and solve this equation to see how many solutions are for this equation.

We need to have x on one side of the equation and everything on the opposite side of x.

1/2(4x - 9) = 2x + 8 ; Start
2x - 4.5 = 2x + 8     ; Distribute the 1/2 across 4x and -9
2x = 2x + 12.5        ; Add 4.5 to each side of the equation
0 = 12.5                  ; Subtract 2x from each side of the equation

As we can clearly see, this equation has 0 answers.