Problem 5 - Algebra 1

Question

Match the verbal phrase with its corresponding algebraic expression. A. \(4 x-11\) B. \(4(x-11)\) c. \(11-4 x\) D. \(11 x+4\) Eleven decreased by the quantity four times a number \(x\)

Step-by-Step Solution

Answer

The verbal phrase 'Eleven decreased by the quantity four times a number \(x\)' translates to the algebraic expression \(11-4x\).

Step 1: Identify Key Words

Find key words in the verbal phrase. In 'Eleven decreased by the quantity four times a number \(x\)', 'decreased by' indicates subtraction and 'four times a number' implies multiplication.

Step 2: Create a Mental Map

'Eleven decreased by the quantity four times a number \(x\)': This can be interpreted as 'We have 11 and we subtract four times some number \(x\) from it'.

Step 3: Match With Given Expressions

Look at the given algebraic expressions A. \(4 x-11 \), B. \(4(x-11)\), C. \(11-4x\), D. \(11 x+4 \) and match with your mental map. Here, C. \(11-4x\) fits with the verbal description.

Key Concepts

Understanding Verbal Phrases

When we talk about verbal phrases in mathematics, we refer to descriptive snippets that represent mathematical operations and expressions in words. For example, the phrase "Eleven decreased by the quantity four times a number \(x\)" is a verbal phrase. It contains clues about which mathematical operations we need to perform. The phrase "decreased by" hints at subtraction, whereas "four times a number" signals multiplication. Recognizing these key words is essential because they guide us in translating verbal phrases into mathematical expressions. Doing so allows us to write out an equation or expression that accurately represents the verbal description, paving the way to solve math problems effectively.

Matching Expressions to Verbal Descriptions

Once you've decoded the verbal phrase, the next step is to match it to its corresponding algebraic expression. Algebraic expressions are equations that use numbers, variables, and often operations (like addition or subtraction) to represent a situation. In our exercise, the goal was to match the verbal phrase "Eleven decreased by the quantity four times a number \(x\)" with one of the given expressions.

In this example, we determined that the phrase "Eleven decreased by" matches with subtracting \(4x\) from \(11\), making it expression C, \(11-4x\). A strong understanding of which words correlate to which operations allows us to make the correct match. Once matched, these algebraic expressions can be used in equations to find solutions to problems involving variables.

Subtraction and Multiplication in Algebraic Expressions

Subtraction and multiplication are fundamental operations in algebra that we frequently encounter.

• **Subtraction:** In the exercise, 'decreased by' signals that we need to perform subtraction. For instance, subtracting the product of a number is often indicated by 'quantity' before the mathematical term. Here, "Eleven decreased by..." results in \(11 - \) some other value.
• **Multiplication:** The phrase "four times a number \(x\)" tells us to multiply. It signifies multiplying the number, in this case four, by the variable \(x\). Thus, it translates to \(4 \times x\) or simply \(4x\).

Once you've identified these operations in a phrase, assembling them into an algebraic expression becomes much more straightforward. Understanding how these simple yet powerful operations fit together forms the backbone of translating verbal phrases into useful mathematical expressions.