Problem 57 - Algebra 1

Question

EQUATIONS AND INEQUALITIES Match the verbal sentence with its mathematical representation. The product of 16 and \(x\) is equal to 32

Step-by-Step Solution

Answer

The mathematical representation of the verbal sentence is: \(16x = 32\).

Step 1: Identify the Operation

In the given sentence 'The product of 16 and \(x\) is equal to 32', the operation mentioned is 'product', which signifies multiplication.

Step 2: Identify the Variables

The letter \(x\) in the algebraic equation represents the unknown number that needs to be found.

Step 3: Formulate the Mathematical Representation

The entire sentence can be expressed as the equation: '16 times \(x\) is equal to 32', which translates into the algebraic equation: \(16x = 32\).

Key Concepts

Equations and Inequalities

Understanding the concept of equations and inequalities is vital when studying algebra, as they are foundational elements of the subject. An equation is a mathematical statement asserting that two expressions have the same value, represented by the equal sign (\(=\)). For example, in the sentence 'The product of 16 and \(x\) is equal to 32', we are implicitly understanding that two quantities are equal to each other – the product of 16 and a number \(x\), and the number 32.