Problem 50 - Algebra and Trigonometry

Question

True or false. $$0 \geq-13$$

Step-by-Step Solution

Answer

True, 0 is greater than or equal to -13.

Step 1: Understanding the inequality

In an inequality, we check if one value is greater than, less than, or equal to another value. In this case, we are asked to evaluate if 0 (zero) is greater than or equal to -13. In the number line, negative numbers are always less than positive numbers and zero.

Step 2: Evaluating the inequality

Here, 0 is compared with -13. Since zero is greater than any negative number, 0 is indeed greater than -13.

Key Concepts

Inequality Evaluation

Inequality evaluation is an essential concept in understanding how numbers relate to each other. When we evaluate inequalities, we determine the relationship between two values. Inequalities typically involve expressions like "greater than," "less than," or "equal to." In the context of the original exercise, we focus on the evaluation of the statement:

• Is 0 greater than or equal to -13?

To solve an inequality problem, carefully compare the given values. Use the knowledge of how numbers are ordered on the number line. Here, the goal is to decide whether the inequality holds true. Showing these comparisons helps develop intuition about numbers and their relationships. Through evaluating inequalities, we can make informed decisions about which values satisfy certain conditions.

Negative Numbers

Understanding negative numbers is crucial when working with inequalities. Negative numbers are numbers less than zero. They lie to the left of zero on the number line. To make sense of comparisons involving negative numbers, remember:

• Negative numbers are always less than positive numbers and zero.
• Among negative numbers, the one with the smaller absolute value is greater (e.g., -1 is greater than -13).

Using these facts can simplify the evaluation of inequalities involving negative numbers. In our example, 0 (zero) is a non-negative number and any non-negative number will be greater than any negative number. Therefore, 0 is definitely greater than -13, supporting our inequality statement.

Number Line Concepts

The number line is a visual tool that helps us understand the order of numbers. It is a straight horizontal line with numbers placed at intervals. Considering inequalities on a number line can help visualize:

• The positioning of negative and positive numbers with relation to zero.
• How to compare values by seeing which lies to the right or left of another.

Numbers increase in value from left to right. Hence, any number placed to the right on this line is greater than a number to its left. Zero is placed at the central point of the number line, and all positive numbers are to its right. All negative numbers are to its left. Using the number line concept, it's immediately visible that 0, being on the right of -13, is indeed greater.