Problem 3 Classify each equation or inequa... [FREE SOLUTION]

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Chapter 15: Problem 3

Classify each equation or inequality as true or false. $$ -10<-1 $$

Short Answer

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True

Step by step solution

Understand the Inequality

The inequality given is $-10 < -1$. This inequality compares two negative numbers.

Compare the Numbers

When comparing negative numbers, it helps to remember that a larger negative number is actually smaller in value. For example, -10 is less than -1.

Make the Determination

Since $-10$ is indeed less than $-1$, the inequality $-10 < -1$ is true.

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Key Concepts

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

Negative Numbers

Negative numbers can often be confusing, but they're important to understand! When we talk about negative numbers, we are talking about numbers that are less than zero. Negative numbers are represented with a minus sign (-). For example, -2, -53, and -1042 are all negative numbers.

Understanding negative numbers is crucial because they come up frequently in math, especially in problems involving inequalities and comparisons. A key fact to remember is that the further you go from zero in the negative direction, the smaller the number gets. This means -10 is smaller than -1 because it is further left on the number line.

True or False Inequalities

An inequality is a comparison between two numbers or expressions using signs such as < (less than), > (greater than), 鈮� (less than or equal to), or 鈮� (greater than or equal to). When determining if an inequality is true or false, you are checking if the statement correctly describes the relationship between the two numbers.

For example, consider the inequality $-10 < -1$. Here, we need to check if -10 is indeed less than -1. Since -10 is further left on the number line than -1, this statement is true.

Another example could be $-3 > -5$. By comparing these numbers, we see that -3 is to the right of -5 on the number line, making this statement true as well.

Number Comparison

Comparing numbers is a foundational skill in math. When comparing numbers, we determine which is larger or smaller. With positive numbers, this is straightforward: 5 is greater than 2, for instance. However, comparing negative numbers can be trickier.

When comparing negative numbers, remember that a number with a larger absolute value is actually smaller. Absolute value is the distance a number is from zero, regardless of direction. So, while |10| = 10 and |-1| = 1, since 10 is further from zero, -10 is less than -1.

-5 and -2: Here, -5 is less than -2 because it is further left.
-7 and -3: Here, -7 is less than -3 for the same reason.

Understanding these concepts makes solving inequalities easier and improves your overall math skills.

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91影视

Classify each equation or inequality as true or false. $$ -10<-1 $$

Short Answer

Step by step solution

Understand the Inequality

Compare the Numbers

Make the Determination

Key Concepts

Negative Numbers

True or False Inequalities

Number Comparison

One App. One Place for Learning.

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