First, we can write:
#x = 0.2bar3#
Next, we can multiply each side by #10# giving:
#10x = 2.3bar3#
Then we can subtract each side of the first equation from each side of the second equation giving:
#10x - x = 2.3bar3 - 0.2bar3#
We can now solve for #x# as follows:
#10x - 1x = (2.3 + 0.0bar3) - (0.2 + 0.0bar3)#
#(10 - 1)x = 2.3 + 0.0bar3 - 0.2 - 0.0bar3#
#9x = (2.3 - 0.2) + (0.0bar3 - 0.0bar3)#
#9x = 2.1 + 0#
#9x = 2.1#
#(9x)/color(red)(9) = 2.1/color(red)(9)#
#(color(red)(cancel(color(black)(9)))x)/cancel(color(red)(9)) = 10/10 xx 2.1/color(red)(9)#
#x = 21/90#
#x = (3 xx 7)/(3 xx 30)#
#x = (color(red)(cancel(color(black)(3))) xx 7)/(color(red)(cancel(color(black)(3))) xx 30)#
#x = 7/30#