Certainly! Let's solve the equation [tex]\( n - 2y = \frac{3y - n}{m} \)[/tex] step by step for the given values [tex]\( y = 5 \)[/tex] and [tex]\( m = -3 \)[/tex].
First, we substitute [tex]\( y \)[/tex] and [tex]\( m \)[/tex] into the equation:
[tex]\[ n - 2(5) = \frac{3(5) - n}{-3} \][/tex]
Simplifying inside the equation:
[tex]\[ n - 10 = \frac{15 - n}{-3} \][/tex]
Next, we need to clear the denominator by multiplying both sides of the equation by [tex]\(-3\)[/tex]:
[tex]\[ -3(n - 10) = 15 - n \][/tex]
Expand and simplify the left-hand side:
[tex]\[ -3n + 30 = 15 - n \][/tex]
Now, combine like terms by moving all terms involving [tex]\( n \)[/tex] to one side of the equation:
[tex]\[ -3n + n + 30 = 15 \][/tex]
Simplify:
[tex]\[ -2n + 30 = 15 \][/tex]
Next, isolate the term with [tex]\( n \)[/tex] by subtracting 30 from both sides:
[tex]\[ -2n = 15 - 30 \][/tex]
[tex]\[ -2n = -15 \][/tex]
Finally, solve for [tex]\( n \)[/tex] by dividing both sides by [tex]\(-2\)[/tex]:
[tex]\[ n = \frac{-15}{-2} \][/tex]
[tex]\[ n = 7.5 \][/tex]
Therefore, the value of [tex]\( n \)[/tex] is [tex]\( 7.5 \)[/tex].
