First, expand the terms in parenthesis on each side of the equation by multiplying each term in the parenthesis by the term outside the parenthesis:
#(color(red)(1/3) * 90x) - (color(red)(1/3) * 12) = (color(blue)(1/2) * 8x) + (color(blue)(1/2) * 10)#
#30x - 4 = 4x + 5#
Now we can add and subtract the necessary terms 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:
#30x - 4 + color(red)(4) - color(blue)(4x) = 4x + 5 + color(red)(4) - color(blue)(4x)#
#30x - 0 - color(blue)(4x) = 4x - color(blue)(4x) + 9#
#30x - color(blue)(4x) = 0 + 9#
#30x - color(blue)(4x) = 9#
Next, we combine the #x# terms on the left side of the equation:
#(30 - 4)x = 9#
#26x = 9#
Finally, we solve for #x# while keeping the equation balanced by dividing each side of the equation by #color(red)(26)#:
#(26x)/color(red)(26) = (9)/color(red)(26)#
#(color(red)(cancel(color(black)(26)))x)/cancel(color(red)(26)) = (9)/color(red)(26)#
#x = 9/26#
