Answer:
The value of x is, [tex]x= \frac{17N+r}{34-N}[/tex]
Explanation:
Given: [tex]N(17+x)=34x-r[/tex]
Distributive Property states that when a number is multiplied by the sum of two numbers, the first number can be distributed to both of those numbers and multiplied by each of them separately.
If [tex]a\cdot(b+c) =a\cdot b + a\cdot c[/tex]
Now, using distributive property on left hand side of the given expression as:
[tex]N\cdot 17+N\cdot x = 34x-r[/tex] or [tex]17N+Nx = 34x-r[/tex]
Addition Property of equality state that we add the same number from both sides of an equation.
Add r to both sides of an equation:
[tex]17N+Nx+r=34x-r+r[/tex]
Simplify:
[tex]17N+Nx+r=34x[/tex]
Subtraction Property of equality state that we subtract the same number from both sides of an equation.
Subtract Nx from both sides of an equation;
[tex]17N+Nx+r-Nx=34x-Nx[/tex]
Simplify:
[tex]17N+r=34x-Nx[/tex]
or
[tex]17N+r=x(34-N)[/tex]
Division Property of equality states that we divide the same number from both sides of an equation.
Divide by (34-N) to both sides of an equation;
[tex]\frac{17N+r}{34-N}= \frac{x(34-N)}{34-N}[/tex]
On Simplify:
[tex]x= \frac{17N+r}{34-N}[/tex]
Solving for x in the equation; n(17+x)=34x−r; we have; x =(17n +r)/(34 -n)
The given equation is; n(17+x)=34x−r
By expansion of the parenthesis;
Divide both sides of the equation by (34 -n)
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