Answer :
Certainly! Let's solve the given equation for \( x \) step by step.
### Given Equation:
[tex]\[ n \cdot (17 + x) = 34x - r \][/tex]
First, expand the left-hand side of the equation:
[tex]\[ n \cdot 17 + n \cdot x = 34x - r \][/tex]
This simplifies to:
[tex]\[ 17n + nx = 34x - r \][/tex]
Next, we need to isolate \( x \). Let's move all terms involving \( x \) to one side of the equation and constant terms to the other:
[tex]\[ 17n + nx - 34x = -r \][/tex]
Now, combine the like terms involving \( x \):
[tex]\[ 17n = 34x - nx + r \][/tex]
Factor out \( x \) on the right-hand side:
[tex]\[ 17n = x(34 - n) + r \][/tex]
Now, solve for \( x \) by dividing both sides by \( (34 - n) \):
[tex]\[ x = \frac{17n + r}{34 - n} \][/tex]
### Solution:
[tex]\[ x = \frac{17n + r}{34 - n} \][/tex]
So, the value of \( x \) in terms of \( n \) and \( r \) is:
[tex]\[ x = \frac{17n + r}{34 - n} \][/tex]
### Given Equation:
[tex]\[ n \cdot (17 + x) = 34x - r \][/tex]
First, expand the left-hand side of the equation:
[tex]\[ n \cdot 17 + n \cdot x = 34x - r \][/tex]
This simplifies to:
[tex]\[ 17n + nx = 34x - r \][/tex]
Next, we need to isolate \( x \). Let's move all terms involving \( x \) to one side of the equation and constant terms to the other:
[tex]\[ 17n + nx - 34x = -r \][/tex]
Now, combine the like terms involving \( x \):
[tex]\[ 17n = 34x - nx + r \][/tex]
Factor out \( x \) on the right-hand side:
[tex]\[ 17n = x(34 - n) + r \][/tex]
Now, solve for \( x \) by dividing both sides by \( (34 - n) \):
[tex]\[ x = \frac{17n + r}{34 - n} \][/tex]
### Solution:
[tex]\[ x = \frac{17n + r}{34 - n} \][/tex]
So, the value of \( x \) in terms of \( n \) and \( r \) is:
[tex]\[ x = \frac{17n + r}{34 - n} \][/tex]
