First, add color(red)(2.7) to each side of the equation to isolate the z term while keeping the equation balanced:
-1.2 + color(red)(2.7) = z/4.6 - 2.7 + color(red)(2.7)
1.5 = z/4.6 - 0
1.5 = z/4.6
Now, multiply each side of the equation by color(red)(4.6) to solve for z while keeping the equation balanced:
color(red)(4.6) xx 1.5 = color(red)(4.6) xx z/4.6
6.9 = cancel(color(red)(4.6)) xx z/color(red)(cancel(color(black)(4.6)))
6.9 = z
z = 6.9
To check the solution we need to substitute 6.9 for z in the original problem and calculate the right side of the equation to ensure it equals -1.2
-1.2 = 6.9/4.6 - 2.7
-1.2 = 1.5 - 2.7
-1.2 = -1.2
Because both sides of the equation equal -1.2 we have verified the solution we obtained is correct.
