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

2 Answers
Jan 30, 2018

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)

Jan 30, 2018

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!