Problem 56 - Algebra 1

Question

EQUATIONS AND INEQUALITIES Match the verbal sentence with its mathematical representation. The sum of \(x\) and 16 is less than 32.

Step-by-Step Solution

Answer

The mathematical representation for the given verbal sentence is \(x + 16 < 32\)

Step 1: Identify Mathematical Meanings

In this problem, we need to translate verbal sentences into mathematical sentences. Here, we have a few key terms. 'The sum'; Sum signifies addition in mathematics. 'of x and 16'; means we are adding x and 16. 'is less than 32' denotes inequality and it specifies that the result of addition is less than 32

Step 2: Form the Equation

Combining all the meanings from the key terms in step1, the sentence 'The sum of \(x\) and 16 is less than 32' can be written as \(x + 16 < 32\)

Key Concepts

Verbal Sentences

Verbal sentences are how we naturally communicate ideas in everyday language. These sentences often describe mathematical concepts in a way that is intuitive to our spoken language. They play a crucial role in math because they are the bridge between real-world situations and algebraic expressions. In this example, the verbal sentence is "The sum of \(x\) and 16 is less than 32."

Let's break this down:

• "The sum of \(x\) and 16" implies adding these two values together.
• "is less than" is an indication of an inequality.
• "32" is the value that the sum is being compared to.

Understanding verbal sentences in math helps translate real-world problems into mathematical expressions that can be solved.

Mathematical Sentences

Mathematical sentences use symbols and numbers to represent a concept. They create clear and concise ways to express relationships between quantities. Consider how a verbal sentence is transformed into a mathematical sentence. For example, "The sum of \(x\) and 16 is less than 32" becomes a mathematical inequality.

The mathematical sentence formed from this verbal sentence is \(x + 16 < 32\). Each part of this sentence corresponds to a part of the original verbal sentence:

• The variable \(x\) and the number 16, when added (\(+\)), form the sum.
• The less than symbol (\(<\)) represents the relationship between this sum and 32.

By turning verbal descriptions into mathematical statements, you gain a tool for problem-solving within a universal language.

Translation of Expressions

Translating expressions involves converting verbal sentences into mathematical sentences. This process allows us to visualize and solve problems systematically. When you see a verbal expression like "The sum of \(x\) and 16 is less than 32," you need to identify key terms and phrases.

Here's the translation process:

• "The sum of \(x\) and 16" indicates an addition, resulting in \(x + 16\).
• The phrase "is less than" tells us to use an inequality symbol \(<\).

Finally, compare the sum to 32 to complete the expression: \(x + 16 < 32\).

Practicing this skill helps effectively communicate complex ideas and allows you to tackle diverse mathematical challenges by transitioning from language to equations.