Sure, let's simplify the expression [tex]\(-n + 4n\)[/tex] using the distributive property. I'll take you through the steps to demonstrate how to arrive at the solution.
1. Identify like terms: In the expression [tex]\(-n + 4n\)[/tex], the terms [tex]\(-n\)[/tex] and [tex]\(4n\)[/tex] are like terms because they both involve [tex]\(n\)[/tex].
2. Combine like terms: We need to combine the coefficients of the like terms.
- The coefficient of the first term [tex]\(-n\)[/tex] is [tex]\(-1\)[/tex].
- The coefficient of the second term [tex]\(4n\)[/tex] is [tex]\(4\)[/tex].
3. Add the coefficients: Now, add the coefficients of the like terms:
[tex]\[
-1 + 4 = 3
\][/tex]
4. Substitute the combined coefficient: Replace the original expression with the combined coefficient and the variable [tex]\(n\)[/tex].
[tex]\[
-n + 4n = (3)n = 3n
\][/tex]
So, the simplified expression is:
[tex]\[
-n + 4n = 3n
\][/tex]
Thus, the solution steps show that:
[tex]\[
-n + 4n = (-1 + 4)n = 3n
\][/tex]
Therefore, the completed expression with the combined terms and simplified result is:
[tex]\[
-n + 4n = (-1 + 4)n = 3n
\][/tex]
