First, isolate the #x# terms on one side of the equation and the constants on the other side of the equation while keeping the equation balanced:
#3.56x + 2.43 color(red)( - 3.56x + 11.40) = 6.17x - 11.40 color(red)( - 3.56x + 11.40) #
#3.56x - 3.56x + 2.43 + 11.40 = 6.17x - 3.56x - 11.40 + 11.40#
#0 + 2.43 + 11.40 = 6.17x - 3.56x - 0#
#2.43 + 11.40 = 6.17x - 3.56x#
#13.83 = (6.17 - 3.56)x#
#13.83 = 2.61x#
Now we can solve for #x# while keeping the equation balanced:
#13.83/color(red)(2.61) = (2.61x)/color(red)(2.61)#
#13.83/2.61 = (color(red)(cancel(color(black)(2.61)))x)/color(red)(cancel(color(black)(2.61)))#
#x = 13.83/2.61#