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!