To solve this problem you first add the necessary terms from each side of the equation to 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:
#4.2x - 4.02 + color(red)( 6.7x) + color(blue)(4.02) = 2.52 - 6.7x + color(red)( 6.7x) + color(blue)(4.02)#
Next step is to group and then combine like terms:
#4.2x + color(red)( 6.7x) - 4.02 + color(blue)(4.02) = 2.52 + color(blue)(4.02) - 6.7x + color(red)( 6.7x)#
#4.2x + color(red)( 6.7x) - 0 = 2.52 + color(blue)(4.02) - 0#
#4.2x + color(red)( 6.7x) = 2.52 + color(blue)(4.02)#
#(4.2 + 6.7)x = 6.54#
#10.9x = 6.54#
Now, to finally solve this problem you divide each side of the equation by #color(red)(10.9)# to solve for #x# while keeping the equation balanced:
#(10.9x)/color(red)(10.9) = 6.54/color(red)(10.9)#
#(color(red)(cancel(color(black)(10.9)))x)/cancel(color(red)(10.9)) = 0.6#
#x = 0.6#
