To create an equivalent expression for the given expression [tex]\(5n + 6 + (-7n)\)[/tex], we should follow these steps to combine the like terms:
1. Identify the like terms:
- Like terms are terms that contain the same variable raised to the same power. In this expression, the like terms include [tex]\(5n\)[/tex] and [tex]\(-7n\)[/tex], as both terms contain the variable [tex]\(n\)[/tex].
2. Combine the like terms with [tex]\(n\)[/tex]:
- Add the coefficients of the like terms:
[tex]\[5n + (-7n)\][/tex]
- Perform the arithmetic operation on the coefficients:
[tex]\[5 + (-7) = -2\][/tex]
- So, the combined term is:
[tex]\[-2n\][/tex]
3. Write down the constant term:
- The constant term in the expression is [tex]\(6\)[/tex], which remains unchanged.
4. Combine the simplified like terms and the constant:
- The expression simplifies to:
[tex]\[-2n + 6\][/tex]
Therefore, the equivalent expression for [tex]\(5n + 6 + (-7n)\)[/tex] is:
[tex]\[ -2n + 6 \][/tex]
