Question

How do you solve and check your solution given `4.1p=16.4`?

Answer 1

See a solution process below:

Explanation:

Divide each side of the equation by `color(red)(4.1)` to solve for `p` while keeping the equation balanced:

`(4.1p)/color(red)(4.1) = 16.4/color(red)(4.1)`

`(color(red)(cancel(color(black)(4.1)))p)/cancel(color(red)(4.1)) = 4`

`p = 4`

To check our solution we need to substitute `4` for `p` in the original equation and ensure both sides of the equation are equal.

`4.1p = 16.4` becomes:

`4.1 xx 4 = 16.4`

`16.4 = 16.4`

Because both sides of the equation are equal we know our solution is correct.

Answer 2

`p = 16.4/4.1`

`p = 4`

`p xx 4.1 = 16.4`

`4 xx 4.1 = 16.4`

`16.4 = 16.4`

Explanation:

We know that:

`p xx 4.1 = 16.4`

If we divide both sides by `4.1` we get

`(p xx 4.1) / 4.1 = 16.4 / 4.1`

We can cancel out both `4.1`s on the left side of the equation - because if we multiply `p` by any number and then divide `p` by that number the answer is just `p`.

`p = 16.4/4.1`

`p = 4`

We can check this is true by replacing `p` with `4` in the original question. If both sides are equal, then we have found the right answer.

`p xx 4.1 = 16.4`

`4 xx 4.1 = 16.4`

`16.4 = 16.4`