Determine the total number of real values of x satisfying this equation:

⌊x⌋ + 2 {-x} = 3x

Notes:
• ⌊N⌋ is floor of N, which is equal to the greatest integer less than or equal to N.
{N} = N - ⌊N⌋.
• Computer program/excel solver assisted solutions are welcome, but a semi-analytic (hand calculator and p&p) methodology is preferred.