Problem 46 - Algebra and Trigonometry

Question

True or false. $$-13<-5$$

Step-by-Step Solution

Answer

True. -13 is less than -5.

Step 1: Understanding Number Line

On a number line, if you move right, the value increases. So, values on the left are always smaller than values on the right. This is how inequality works in numerical comparisons.

Step 2: Compare the Values

Now, -13 is to the left of -5 on the number line simply because it is a smaller value. This confirms that -13 is indeed less than -5.

Key Concepts

Number Line

When dealing with math problems, visualizing numbers on a number line can greatly enhance your comprehension of numerical relationships. Imagine a horizontal line with zero in the middle, negative numbers to the left, and positive numbers to the right. Each point on this line corresponds to a unique number.

As a rule of thumb, as you move rightwards from zero, numbers increase in value. Conversely, as you move leftwards, numbers decrease. This visual representation is crucial for understanding inequalities because it allows you to clearly see which numbers are greater or smaller by their position on the line. For example, the location of -13 is to the left of -5, indicating that -13 is indeed less than -5.

Numerical Comparisons

Numerical comparisons are at the heart of understanding math problems. In our daily life, we compare quantities to make decisions, like who has more pieces of cake. Mathematically, we use symbols such as <, >, ≤, and ≥ to compare numbers directly.

For the example at hand, we assess which of the two numbers, -13 or -5, is smaller. Since the number line shows -13 to the left of -5, we conclude that -13 is less than -5. We use the < symbol to represent this relationship, writing it as \( -13 < -5 \). In essence, comparing numbers helps build the foundation of mathematical understanding, enabling us to solve more complex problems.

Understanding Inequalities

Inequalities are statements about the relative size or order of two values. They tell us whether one number is greater than, less than, or possibly equal to another number but not exactly equivalent. Understanding inequalities is essential for solving simple to complex mathematical problems.

For instance, in the statement \( -13 < -5 \), the symbol ' < ' signifies 'is less than,' highlighting that -13 is not as large as -5. Being familiar with inequality symbols helps us quickly convey mathematical relationships and opens the door to exploring solutions in domains such as algebra, where inequalities often define ranges of possible values.