Problem 1 - Algebra 1

Question

Write an inequality for the sentence: Three is greater than negative five.

Step-by-Step Solution

Answer

The inequality for the sentence 'Three is greater than negative five' is \(3 > -5\).

Step 1: Identify Values

Identify the numbers in the sentence: 'Three' corresponds to the number 3, and 'negative five' corresponds to the number -5.

Step 2: Understand Comparison

The sentence uses the phrase 'is greater than' to compare three and negative five. In inequality, 'greater than' is represented as '>'.

Step 3: Compose Inequality

Shaping up the identified values and the symbol for 'greater than', form the inequality as 3 > -5.

Key Concepts

Inequality Symbols

In mathematics, inequality symbols are fundamental tools used for comparing numbers and expressing their relative sizes. These symbols serve as shorthand notations to describe the relationship between two values. The most common inequality symbols include '<' (less than), '>' (greater than), '' (less than or equal to), and '' (greater than or equal to). Understanding how to use these correctly is crucial in accurately forming and solving inequalities.

For example, when we say that 'a' is greater than 'b', we write it as 'a > b'. Similarly, if 'c' is less than 'd', it is written as 'c < d'. This concise notation is very efficient in communicating comparisons without using words. In solving the problem, 'Three is greater than negative five', we express this relationship using the '>' symbol, forming the inequality '3 > -5'.

Comparing Numbers

Comparing numbers is a foundational concept in math, as it allows us to evaluate the size of numbers relative to one another. It involves determining which of two numbers is larger, which is smaller, or whether they are equal. Comparisons can be made with whole numbers, integers, fractions, and even irrational numbers.

When comparing whole numbers, the process is straightforward—the number with more digits is the larger number, and vice versa. However, when we bring in negative numbers, the comparison requires careful attention to their signs. A positive number is always greater than a negative number. In the context of the exercise, 3 (a positive number) is greater than -5 (a negative number), which is why the inequality 3 > -5 correctly represents their relationship.

Expressing Inequalities

Expressing inequalities is a way to represent the relationship between values that are not equal. This is done using the inequality symbols mentioned earlier. Inequalities are commonly used in various disciplines such as mathematics, economics, and engineering, to demonstrate limits, ranges, and conditions that are not strict equalities.

In an inequality expression, the smaller value is typically written on the left, and the larger value on the right. However, the inequality can be read in both directions by adjusting the inequality symbol: '3 > -5' can also be written as '-5 < 3'. It's essential when expressing inequalities to be consistent with the direction of the inequality symbol to convey the correct meaning. For instance, writing '3 < -5' would incorrectly indicate that 3 is less than -5, which is not the intended expression of the original statement.