Question

How do you solve and check your solutions to `3.2+x/2.5=4.6`?

Answer 1

See the entire solution and verification process below:

Explanation:

First, subtract `color(red)(3.2)` from each side of the equation to isolate the `x` term while keeping the equation balanced:

`3.2 + x/2.5 - color(red)(3.2) = 4.6 - color(red)(3.2)`

`3.2 - color(red)(3.2) + x/2.5 = 1.4`

`0 + x/2.5 = 1.4`

`x/2.5 = 1.4`

Now, multiply each side of the equation by `color(red)(2.5)` to solve for `x` while keeping the equation balanced:

`color(red)(2.5) xx x/2.5 = color(red)(2.5) xx 1.4`

`cancel(color(red)(2.5)) xx x/color(red)(cancel(color(black)(2.5))) = color(red)(2.5) xx 1.4`

`x = 3.5`

To verify the solution we substitute `3.5` for `x` in the left side of the equation and calculate to ensure the left side of the equation is equal to the right side of the equation:

`3.2 + x/2.5 = 4.6` becomes:

`3.2 + 3.5/2.5 = 4.6`

`3.2 + 1.4 = 4.6`

`4.6 = 4.6`

Because both sides of the equation are equal `x = 1.4` is a valid solution.