How many solution are there to this equation

Hmmm... IDK.

Checking cases, there is only one solution: x = -8:

For x = -8, |x| = 8

-1/2*x + 4 = (-1/2)*(-8) + 4 = 4 + 4 = 8

Therefore, x = -8 is the only solution.

The graph of |x|  is V shaped, two lines radiating upwards, from the origin, at 45 deg  to the horizontal.

-x/2 + 4 is a straight line crossing the vertical axis at 4 and with a slope of -1/2.

The solutions of the equation are the x co-ordinates of the points of intersection of the two graphs, there are two of them.

The one on the left is at x = -8.

Leave you to find the one to the right of the origin.

There are two solutions to the equation:

| x | = (-1/2)x + 4

By rearranging the terms, we get:

x + (1/2)x = 4

Simplifying:

(3/2)x = 4

x = 8/3 or

x = -8

Therefore, the two solutions to the equation are x = 8/3 and x = -8.