Question

Solve for xx2 - 3|x - 2| - 4x = - 6​

Answer 1

Answer:

x = 0, 1, 3, 4.

Step-by-step explanation:

$x^2 -3|x-2| -4x=-6$

Now the Modulus will open with + or - depending on wether x is greater or less than 2.

Case 1: x > 2

modulus opens with + sign

$x^2-3(x-2)-4x=-6\\x^2 - 7x +12 =0\\(x-3)(x-4) = 0\\x=3,4$

Case 2: x < 2

modulus opens in - sign

$x^2 -3(2-x)-4x=-6\\x^2-x=0\\x(x-1)=0\\x=0,1$

So the solutions are x = 0, 1, 3, 4.