Problem 54 - Elementary Algebra

Question

True or false. $$ -5>-10 $$

Step-by-Step Solution

Answer

True.

Step 1: Understanding the Inequality

The problem presents the inequality \(-5 > -10\). This asks if \(-5\) is greater than \(-10\). To solve, we need to compare these two negative numbers on a number line.

Step 2: Analyzing the Number Line

On a number line, numbers increase in value as they move from left to right. When dealing with negative numbers, the number that is less negative is actually greater. So, \(-5\) is to the right of \(-10\) on a number line.

Step 3: Comparing the Values

Because \(-5\) is to the right of \(-10\), \(-5\) is indeed larger than \(-10\). Therefore, the statement \(-5 > -10\) is true.

Key Concepts

Understanding Negative Numbers

Negative numbers are the numbers that appear on the left of zero on the number line. The further you go left, the more negative the numbers become. This is the opposite of positive numbers, which are on the right of zero.
Understanding negative numbers is crucial because they obey some unique rules compared to positive numbers. For example, adding a negative number is like subtracting the corresponding positive number.
Another important aspect is that when multiplying or dividing two negative numbers, the result is positive. However, if you multiply or divide a positive number by a negative number, the result will be negative. Negative numbers are less than zero, but remember, a smaller negative number (in terms of absolute value) is actually greater than a larger negative number (because it is closer to zero).

Using the Number Line to Compare

The number line is a visual representation of numbers in a straight line. It helps us to see the relative position of numbers and thus compare them easily.

• Moving right on the number line means the numbers are increasing.
• Moving left means the numbers are decreasing.

Negative numbers are positioned to the left of zero, and positive numbers to the right. This visual cue makes it easy to compare numbers, especially negative ones.
When comparing negative numbers, the value closest to zero on the number line is the larger one. For example,

Example Comparison on the Number Line

Think of you have the numbers you you need to compare -3 and -7, you can see that -3 is to the right of -7, making -3 the greater number.

Comparing Values of Negative Numbers

Comparing values, especially negative numbers, may seem tricky. However, always remember:

• In a set of negative numbers, the number with the smallest absolute value is the largest because it is closest to zero.
• For instance, between -5 and -10, -5 has a smaller absolute value, thus it is greater than -10.

When we say one number is greater than another, on the number line, it is further to the right. Sometimes using reference points like zero helps; negative numbers closer to zero are greater.
Here's a handy tip: when faced with two negative numbers, cover up their negative signs and compare as if they were positive. The original number with the bigger absolute value will actually be the smaller number when negative. This trick often simplifies the comparison process.