to clear the fractions multiply by a common denominator of 12x on both sides..
so the equation becomes 4 - 6x = -3 - 4x
add 6x to both sides... 4 = -3+2x
add 3 to both sides... 7 = 2x
divide both sides by 2.. x = 7/2 or 3.5
(unless the x should not have been in the denominator as shown in your statement.)