How many solution are there to this equation

\( |x| = -\dfrac 1 2 x + 4?\)

coolkidslovemath1982 Mar 15, 2023

#2**0 **

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.

Guest Mar 15, 2023

#5**0 **

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.

Guest Mar 15, 2023