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

Verified step by step guidance

1. Identify the components of the phrase: 'the product of six and a number' can be expressed as \(6x\), where \(x\) is the number.
2. Identify the second component: 'negative two times the number' can be expressed as \(-2x\).
3. The phrase 'the difference between' indicates subtraction, so we set up the expression as \(6x - (-2x)\).
4. Simplify the expression by recognizing that subtracting a negative is equivalent to addition: \(6x + 2x\).
5. Combine like terms to simplify the expression further: \(8x\).

Key Concepts

Algebraic Expressions

An algebraic expression is a mathematical phrase that can include numbers, variables, and operation symbols. In this context, it represents a relationship or operation involving a variable, such as 'x'. Understanding how to translate English phrases into algebraic expressions is crucial for solving algebra problems.

Product and Difference

The product refers to the result of multiplying two or more numbers or expressions, while the difference is the result of subtracting one number from another. In the given question, recognizing how to express 'the product of six and a number' and 'the difference' between two expressions is essential for forming the correct algebraic expression.

Simplification of Expressions

Simplification involves reducing an algebraic expression to its simplest form by combining like terms and performing operations. This process is important for making expressions easier to work with and understand. In this exercise, after forming the algebraic expression, simplifying it will help clarify the relationship between the variables involved.