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Chapter 1: Problem 103

Translate to an inequality. A number \(a\) is negative.

Short Answer

Expert verified
a < 0

Step by step solution

01

Understand the Condition

To translate the given statement into an inequality, first understand what it means for a number to be negative. A negative number is any number that is less than zero.
02

Identify the Variable

In this problem, the number is represented by the variable 'a'.
03

Write the Inequality

Combine the understanding from Step 1 (negative numbers are less than zero) and Step 2 (the variable is 'a'). This gives the inequality: a < 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 values found to the left of zero on a number line. They are always smaller than zero.
For example, -1, -2, and -100 are negative numbers.
In mathematics, we often compare values, and knowing whether a number is negative is critical for these comparisons.
If we need to express that a variable represents a negative number, we say it is less than zero. This concept helps us understand and solve inequality problems.
variables
Variables are symbols, often letters, used to represent numbers in equations and inequalities.
In our problem, the variable is represented by 'a'. Variables make it easier to work with general numbers or unknown values in mathematics.
Using variables allows us to write expressions and equations in a simplified form. It's like using a placeholder that can stand for any number. In our example, 'a' is the placeholder for a number that is negative. Once we know that 'a' is negative, we can work with it just as we would with other numbers.
writing inequalities
An inequality is a mathematical sentence that shows the relationship between quantities that are not equal.
Inequalities use symbols like <, >, 鈮�, and 鈮� to compare values.
In this particular problem, we translate the phrase 'a number is negative' into an inequality.
Since we know negative numbers are less than zero and our variable is 'a', we can write the inequality as:
\( a < 0 \).
This communicates that 'a' is any number that is less than zero. Combining all the steps makes translating English statements to mathematical expressions straightforward.

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Most popular questions from this chapter

Translate to an inequality. When Helga's calculator gives a decimal value for \(\sqrt{2}\) and that value is promptly squared, the result is \(2 .\) Yet when that same decimal approximation is entered by hand and then squared, the result is not exactly \(2 .\) Why do you suppose this is?

Write an equivalent expression without using grouping symbols. $$ -(4 a-3 b+7 c) $$

Simplify. $$ 8(-7)+|6(-5)| $$

Simplify. $$ 8 n^{2}-3 n+2\left(n-4 n^{2}\right) $$

Simplify. $$ -8 a^{2}+5 a b-12 b^{2}-6\left(2 a^{2}-4 a b-10 b^{2}\right) $$
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