Simplify each expression. See Example 8.-6p + 5 - 4p + 6 + 11p

Verified step by step guidance

1. Combine like terms by grouping the terms with 'p' together: \(-6p - 4p + 11p\).
2. Combine the constant terms: \(5 + 6\).
3. Simplify the expression with 'p': \(-6p - 4p + 11p = (11 - 6 - 4)p\).
4. Simplify the constant terms: \(5 + 6 = 11\).
5. Combine the simplified terms to get the final expression.

Key Concepts

Combining Like Terms

Combining like terms is a fundamental algebraic process where terms with the same variable and exponent are added or subtracted. In the expression -6p + 5 - 4p + 6 + 11p, the terms -6p, -4p, and 11p are like terms because they all contain the variable 'p'. This process simplifies the expression by consolidating these terms into a single term.

Order of Operations

The order of operations is a set of rules that dictates the sequence in which mathematical operations should be performed to ensure consistent results. Commonly remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction), this principle is crucial when simplifying expressions to avoid errors in calculations.

Constant Terms

Constant terms are numerical values in an expression that do not contain any variables. In the given expression, the constants are 5, 6, and any other standalone numbers. When simplifying, these constants can be combined to produce a single constant term, which contributes to the overall simplification of the expression.