The question is "State with a reason whether there are any solutions to |12-5x| = -2x+3"
I can clearly see there are no solutions when I graph it but I've learned to solve these questions doing the following:
$|x| = y$
$x = y $
$x = -y $
When doing this here, I get:
$|12 - 5x| = -2x + 3$
$12 - 5x = -2x + 3$
$12 - 5x = 2x - 3$
Solving for each of these I get $(3, -3)$ -> So no solution here as the y is negative - makes sense
But I also get $(15/7, 9/7)$ which would, in theory be an intersection.
Obviously this isn't right but algebraically I'm having trouble with the intuition.
Hope someone can help!