Problem 13 - Prealgebra

Question

Write each of the following in symbols. \(-3\) is greater than \(-15\)

Step-by-Step Solution

Answer

The inequality symbolically is \(-3 > -15\).

Step 1: Understanding the Problem

We need to translate the statement "-3 is greater than -15" into a mathematical inequality involving symbols.

Step 2: Identifying Mathematical Symbols

In mathematics, the phrase "is greater than" corresponds to the symbol `>`.

Step 3: Translating Words to Symbols

Replace the words with their corresponding mathematical symbols: 'is greater than' is replaced by '>', and the numbers remain the same. Thus, we write: \[-3 > -15\].

Key Concepts

Mathematical Inequalities

Mathematical inequalities are statements indicating that two values are not equal and show the relationship between them. This is an essential part of mathematics because it helps to compare quantities and solve problems that involve ranges of possible values. In simple terms, inequalities show how two numbers or expressions relate to each other in size or order. Common inequality symbols include:

• \(>\) (greater than)
• \(<\) (less than)
• \(\geq\) (greater than or equal to)
• \(\leq\) (less than or equal to)
• \(neq\) (not equal to)

Inequalities are used to define ranges of numbers that satisfy certain conditions. For instance, if we say \(x > 5\), it means that \(x\) can be any number greater than 5 but not equal to 5. Understanding these symbols and their meanings is crucial when translating real-world situations into mathematical language.

Greater Than Symbol

The greater than symbol \(>\) is used to denote that the value on the left side is larger than the value on the right side. It is one of the fundamental building blocks when it comes to inequalities. For instance, when we write \(-3 > -15\), it means that \(-3\) is greater than \(-15\), which might seem counterintuitive because both numbers are negative.Here's a quick tip to remember how the greater than symbol works: imagine that the symbol is like a hungry crocodile mouth always wanting to "eat" the larger value. So, it always opens toward the larger number.Using the greater than symbol is common in comparing values in a number of settings, ranging from simple arithmetic exercises to complex data analysis.

Translating Verbal Statements into Symbols

Translating verbal statements into symbols is an essential skill in mathematics as it allows us to express mathematical ideas succinctly and uniformly. This process involves identifying keywords in a verbal statement and replacing them with appropriate mathematical symbols.Let's take the example "-3 is greater than -15." Breaking it down:

• The number \(-3\) stays the same in symbolic form.
• "Is greater than" translates directly to the symbol \(>\).
• The number \(-15\) also remains unchanged.

So, the statement \(-3 > -15\) is formed by combining these parts together. This translation makes the problem easier to manipulate, solve, and understand, especially in more complex mathematical settings. Being proficient in converting verbal statements greatly enhances problem-solving skills and mathematical literacy.