Question

How do you solve and check your solutions to `-1.2=z/4.6-2.7`?

Answer 1

See the entire solution and verification process below:

Explanation:

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.