Question

How can IExress q in term of p? show the steps p=8-5q/q

Answer 1

See a solution process below:

Assuming the equation is: `p = (8 - 5q)/q`

Otherwise:

`p = 8 - (5q)/q` is the same as: `p = 8 - (5color(red)(cancel(color(black)(q))))/(color(red)(cancel(color(black)(q)))) =>`

`p = 8 - 5 =>`

`p = 3`

Explanation:

First, rewrite the equation as:

`p = 8/q - (5q)/q`

`p = 8/q - (5color(red)(cancel(color(black)(q))))/color(red)(cancel(color(black)(q)))`

`p = 8/q - 5`

Next, add `color(red)(5)` to each side of the equation to isolate the `q` term while keeping the equation balanced:

`p + color(red)(5) = 8/q - 5 + color(red)(5)`

`p + 5 = 8/q - 0`

`p + 5 = 8/q`

Then we can rewrite the equation as:

`(p + 5)/1 = 8/q`

Because each side of the equation is now a pure fraction we can flip the fractions and rewrite the equation as:

`1/(p + 5) = q/8`

Now, multiply each side of the equation by `color(red)(8)` to solve for `q` while keeping the equation balanced:

`color(red)(8) xx 1/(p + 5) = color(red)(8) xx q/8`

`8/(p + 5) = cancel(color(red)(8)) xx q/color(red)(cancel(color(black)(8)))`

`8/(p + 5) = q`

`q = 8/(p + 5)`

Answer 2

`q=8/(p+5)`.

Explanation:

`p=(8-5q)/q=8/q-(5cancelq)/cancelq=8/q-5`.

`"Adding "5, p+5=8/qcancel(-5+5)=8/q, i.e.,`

`(p+5)/1=8/q`,

Taking reciprocals, `1/(p+5)=q/8`.

Multiplying by `8," we have, "8*1/(p+5)=q/8*8, or,`

`q=8/(p+5),` is the desired expression!