How many solution are there to this equation
\( |x| = -\dfrac 1 2 x + 4?\)
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.