In Exercises 121–128, write each English phrase as an algebraic expression. Then simplify the expression. Let x represent the number. Six times the product of negative five and a number

Verified step by step guidance

1. Identify the phrase 'the product of negative five and a number' and express it as an algebraic expression: \(-5x\).
2. Recognize the phrase 'six times' which indicates multiplication by 6.
3. Combine the expressions to represent 'six times the product of negative five and a number' as \(6 \times (-5x)\).
4. Simplify the expression by multiplying the constants: \(6 \times (-5) = -30\).
5. Write the simplified expression as \(-30x\).

Key Concepts

Algebraic Expressions

An algebraic expression is a mathematical phrase that can include numbers, variables, and operation symbols. It represents a value and can be simplified or evaluated. Understanding how to translate verbal phrases into algebraic expressions is crucial for solving problems in algebra.

Variables and Constants

In algebra, a variable is a symbol, often represented by letters like x, that stands for an unknown value. Constants are fixed values, such as numbers. Recognizing the role of variables and constants is essential for forming and manipulating algebraic expressions correctly.

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. The common acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) helps remember this order, which is vital when simplifying algebraic expressions.