Question

have exactly one solution. consider the equation 2n + 6 = 2(3 + n).
n | solution?
0 | solution
1 | solution
2 | solution
3 | solution

the expression 2n + 6 is any value, only some values, no values equal to 2(3 + n).
what values of n make...
the equation is true for ? of n.

Explanation:

Step1: Simplify the right - hand side

We start with the equation \(2n + 6=2(3 + n)\). First, we expand the right - hand side using the distributive property \(a(b + c)=ab+ac\). Here, \(a = 2\), \(b = 3\) and \(c=n\), so \(2(3 + n)=2\times3+2\times n=6 + 2n\).

Step2: Compare both sides

Now our equation becomes \(2n+6 = 2n + 6\). If we subtract \(2n\) from both sides, we get \(2n+6-2n=2n + 6-2n\), which simplifies to \(6 = 6\). This is a true statement regardless of the value of \(n\).

Answer:

The equation is true for any value of \(n\).