First, isolate the #x# terms on the left side of the equation and the constants on the right side of the equation while always keeping the equation balanced:
#4.2x - 1.34 + color(red)( 6.7x + 1.34) = 0.84 - 6.7x + color(red)( 6.7x + 1.34) #
Now rearrange to group like terms:
#4.2x + color(red)( 6.7x) - 1.34 + color(red)(1.34) = 0.84 + color(red)(1.34) - 6.7x + color(red)( 6.7x)#
Next we can combine like terms on each side of the equation:
#(4.2 + 6.7)x - 0 = 0.84 + 1.34 - 0#
#10.9x = 2.18#
Now we can solve for #x# by dividing each side of the equation by #color(red)(10.9)# which will also keep the equation balanced.
#(10.9x)/color(red)(10.9) = 2.18/color(red)(10.9)#
#(color(red)(cancel(color(black)(10.9)))x)/cancel(color(red)(10.9)) = 0.2#
#x = 0.2#
