Problem 28 - Introductory and Intermediate Algebra for College Students 4th

Question

Write each English phrase as an algebraic expression. Let the variable \(x\) represent the number. six less than a number

Step-by-Step Solution

Answer

The algebraic expression for the phrase 'six less than a number' is \(x - 6\).

Step 1: Translate English phrase to Mathematical Expression

The English phrase 'six less than a number' can be translated into a mathematical expression as follows: 1. Identify the number. The 'number' referred to in the phrase is represented by \(x\). 2. Identify the operation. 'less than' is a phrase that indicates subtraction. 3. The 'six less than a number' is therefore \(x-6\). It's the number \(x\) with 6 subtracted from it.

Step 2: Identify the algebraic structure

Determine the type of algebraic problem.

Step 3: Apply algebraic techniques

Use factoring, expanding, or systematic methods.

Step 4: Simplify and solve

Simplify expressions and solve for unknowns.

Step 5: State the result

Write the final answer.

Step 6: Conclude with the answer

The algebraic expression for the phrase 'six less than a number' is \(x - 6\).

Key Concepts

Translation of Phrases

Translating English phrases into algebraic expressions is a common task in mathematics. It involves understanding specific language clues and converting them into symbols that make up mathematical expressions. In this exercise, we focus on the phrase "six less than a number." Here, the key part to recognize is "less than," which suggests a subtraction operation is involved.

A helpful strategy is to imagine the phrase as simpler arithmetic. Start by identifying the number mentioned, here referred to as "a number," which we represent with the letter or variable x. The phrase "less than" signals that you subtract a value from this number. In our example, we subtract six from x.

Converting phrases to algebraic expressions often calls for reversing the typical English order of words. Note how "six less than a number" becomes "x minus 6" in the mathematical expression. This skill comes with practice, and you can sharpen it by translating various phrases into algebraic terms.

Subtraction Operation

Subtraction is one of the foundational operations in mathematics, symbolized by the minus sign (-). In algebra, subtraction often involves removing value from a variable, like subtracting 6 from a number. This operation conforms to the same principles as arithmetic subtraction, where you reduce one quantity by the amount of another.

In the context of our example, the phrase "six less than a number" translates into the subtraction operation \(x - 6\). Here, 6 is the subtrahend, and x is the minuend. The outcome, or the difference, is the result of subtracting 6 from the unknown quantity x.

• Minuend: The starting quantity (\