Certainly! Let's solve the equation step-by-step to find the value of [tex]\( m \)[/tex].
The given equation is:
[tex]\[
\frac{m}{n} + 5m = 20
\][/tex]
First, we'll combine the terms involving [tex]\( m \)[/tex] on one side of the equation:
[tex]\[
\frac{m}{n} + 5m = 20
\][/tex]
To combine the terms, we can factor [tex]\( m \)[/tex] out of the left side. However, let's first bring the fractions to a common denominator:
[tex]\[
\frac{m}{n} + 5m = \frac{m}{n} + \frac{5mn}{n} = \frac{m + 5mn}{n}
\][/tex]
Now, rewrite the equation:
[tex]\[
\frac{m + 5mn}{n} = 20
\][/tex]
To clear the fraction, multiply both sides by [tex]\( n \)[/tex]:
[tex]\[
m + 5mn = 20n
\][/tex]
Now we want to isolate [tex]\( m \)[/tex]. To do this, factor [tex]\( m \)[/tex] out from the left side:
[tex]\[
m (1 + 5n) = 20n
\][/tex]
Now, solve for [tex]\( m \)[/tex] by dividing both sides by [tex]\( 1 + 5n \)[/tex]:
[tex]\[
m = \frac{20n}{1 + 5n}
\][/tex]
Hence, the solution for [tex]\( m \)[/tex] in terms of [tex]\( n \)[/tex] is:
[tex]\[
m = \frac{20n}{1 + 5n}
\][/tex]
So the value of [tex]\( m \)[/tex] is [tex]\( \frac{20n}{1 + 5n} \)[/tex].
