## Algebra 1: Common Core (15th Edition)

$n=1.5$
We first distribute the negative into the parenthesis to get the equation 8n-2n+3=12. This problem now deals with combining like terms. Like terms are terms that have the same variable raised to the same power. Note, by this definition, numbers like 10 and 15 are also like terms as they are multiplied by a variable raised to the zeroth power. This concept may seem confusing, but it makes sense if we consider it for a second. Anything raised to the zeroth power is one. Thus, $x^{0}$ is 1. Earlier in the chapter, we learned the Identity Property of Multiplication, which states that anything times one is itself. Thus, 15 is equal to 15$x^{0}$ because $x^{0}$ is equal to 1. Now, back to the problem. Recall, if terms are like terms, we can add or subtract these terms just like we add or subtract numbers. Thus, because 8n and -2n are like terms, we can add them to simplify the equation to $6n+3=12$. We now subtract 3 to get that $6n=9$. We divide both sides by 6 to get that $n=9/6$ (which equals 1.5).