Verified Answer :

\(8r-5q=3\) 

\(8r-5q=3:q\) 

\(-5q=3-8r\)  \(|Subtract \ 8r \ from \ both \ sides|\) 

\(q= \dfrac{3-8r}{-5}\)  \(|Divide \ both \ sides \ by \ -5|\) 

\(q= -\dfrac{3-8r}{5}\) 

The solution of the equation for the specified variable (q) is \(q = \frac{8r-3}{5}\) OR \(q = \frac{8r}{5}- \frac{3}{5}\)

For the given equation, 8r-5q=3, to solve for q means we should make q the subject of the equation. To do this, we rearrange the equation so that q stands alone.

Now, from the given equation

8r-5q=3

\(8r-5q=3\)

First, transfer 3 to the left hand side (LHS) of the equation and -5q to the right hand side(RHS) of the equation,

We get

\(8r-3=5q\)

[Note that the sign before 3 (+) changes to (-) and the sign before 5q (-) changes to (+)]

Then, we can write that

\(5q = 8r-3\)

Now, divide both sides by 5

\(\frac{5q}{5} = \frac{8r-3}{5}\)

∴ \(q = \frac{8r-3}{5}\)

This can also be written as

\(q = \frac{8r}{5}- \frac{3}{5}\)

Hence, the solution of the equation for the specified variable (q) is \(q = \frac{8r-3}{5}\) OR \(q = \frac{8r}{5}- \frac{3}{5}\)

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