Question

Write each statement as an inequality. \(z\) is negative

Short answer

\(z < 0\)

Step-by-step solution

Identify the meaning of the statement

The statement says that the variable \(z\) is a negative number. This means that any value of \(z\) must be less than zero.

Write the inequality

Since \(z\) is negative, it must be less than zero. This can be written as the inequality \(z < 0\).

Key concepts

negative numbers

Negative numbers are those numbers that are less than zero. They are found to the left of zero on a number line. For example, -1, -2, and -3 are negative numbers. They are crucial in mathematics because they allow us to represent values below zero, such as temperatures below freezing or elevations below sea level. In inequalities, negative numbers are often compared to zero or other values to express certain conditions, like 'less than zero' which we see in the inequality for this exercise: \( z < 0 \).

variables

Variables are symbols used to represent unknown or changeable values. They are a fundamental part of algebra and are often denoted by letters such as x, y, or z. In the exercise, the variable is z. A variable can take on different values, which makes it versatile in equations and inequalities. For example, in the inequality \(z < 0\), z can be any number that is less than zero, such as -1, -2, -100, etc. Understanding the function and flexibility of variables is key to mastering algebraic concepts.

inequality notation

Inequality notation is a way to show the relationship between two values where they are not equal. Instead of the equality symbol (=), inequalities use symbols like: < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to). For instance, \(z < 0\) means z can be any value less than zero. This notation helps denote ranges of values and conditions that aren't fixed to one specific value. Mastery of inequality notation allows for the expression of more complex mathematical relationships.