To solve this problem you first add the necessary terms from each side of the equation to isolate the xx 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)4.2x−4.02+6.7x+4.02=2.52−6.7x+6.7x+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+6.7x−4.02+4.02=2.52+4.02−6.7x+6.7x
4.2x + color(red)( 6.7x) - 0 = 2.52 + color(blue)(4.02) - 04.2x+6.7x−0=2.52+4.02−0
4.2x + color(red)( 6.7x) = 2.52 + color(blue)(4.02)4.2x+6.7x=2.52+4.02
(4.2 + 6.7)x = 6.54(4.2+6.7)x=6.54
10.9x = 6.5410.9x=6.54
Now, to finally solve this problem you divide each side of the equation by color(red)(10.9)10.9 to solve for xx while keeping the equation balanced:
(10.9x)/color(red)(10.9) = 6.54/color(red)(10.9)10.9x10.9=6.5410.9
(color(red)(cancel(color(black)(10.9)))x)/cancel(color(red)(10.9)) = 0.6
x = 0.6
