Question

not all equations have exactly one solution. consider the equation $2n + 6 = 2(3 + n)$. the expression $2n + 6$ is equivalent to $2(3 + n)$. what values of $n$ make the equation true? the equation is true for? of $n$.

Explanation:

Step1: Expand the right-hand side

$2(3 + n) = 2\times3 + 2\times n = 6 + 2n$

Step2: Compare both sides

Left-hand side: $2n + 6$; Right-hand side: $2n + 6$
Both sides are identical, so simplifying gives $2n + 6 = 2n + 6$, which reduces to $0=0$.

Step3: Interpret the result

A statement $0=0$ is always true, regardless of the value of $n$.

Answer:

All values
The equation is true for all values of n.