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Chapter 0: Problem 26

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

Short Answer

Expert verified
\(z < 0\)

Step by step solution

01

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.
02

Write the inequality

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

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

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), 鈮� (less than or equal to), and 鈮� (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.

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Most popular questions from this chapter

Expressions that occur in calculus are given. Write each expression as a single quotient in which only positive exponents and radicals appear. $$\frac{x}{(1+x)^{1 / 2}}+2(1+x)^{1 / 2} \quad x>-1$$

Simplify each expression. $$100^{3 / 2}$$

Expressions that occur in calculus are given. Write each expression as a single quotient in which only positive exponents and radicals appear. $$\frac{\left(9-x^{2}\right)^{1 / 2}+x^{2}\left(9-x^{2}\right)^{-1 / 2}}{9-x^{2}} \quad-3

Simplify each expression. Assume that all variables are positive when they appear. $$8 x y-\sqrt{25 x^{2} y^{2}}+\sqrt[3]{8 x^{3} y^{3}}$$

Simplify each expression. $$\left(-\frac{64}{125}\right)^{-2 / 3}$$
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