Question

Write each statement as an inequality. \(y\) is greater than -5

Short answer

\( y > -5 \)

Step-by-step solution

Identify the variable and inequality relationship

First, identify the variable and the relationship it has according to the problem statement. Here, the variable is denoted as \( y \), and it is said to be 'greater than' another number.

Determine the inequality sign

Since the statement says \( y \) is 'greater than' -5, the inequality sign that represents 'greater than' is \( > \).

Combine the variable, inequality sign, and number

Finally, combine the variable \( y \) with the inequality sign \( > \) and the number -5 to form the inequality: \( y > -5 \).

Key concepts

Variable Identification

Understanding variables is key in forming and solving inequalities. A variable is a symbol, usually a letter, that represents a number or a set of numbers. In the given exercise, the variable is denoted as y. It's crucial to pinpoint the variable as it tells you what you are comparing to other numbers.

Inequality Sign

The inequality sign is a symbol that shows the relationship between the variable and a number. In our example, we need to determine which sign to use. When the statement mentions 'greater than', it is represented by the symbol $>$. Other common inequality signs include:

• <: less than
• ≤: less than or equal to
• ≥: greater than or equal to

By recognizing the language used in the problem, you can identify the appropriate inequality sign, which is vital when forming the inequality notation.

Mathematical Notation

Combining the variable, inequality sign, and the number forms a complete mathematical notation. This notation concisely expresses the relationship described in the problem. For example, the statement 'y is greater than -5' can be mathematically denoted as $$y > -5. This concise format is used to solve and graph inequalities, making the relationship clear and easy to understand. Remember, proper mathematical notation is essential for communicating and solving math problems accurately.