Problem 100 - Elementary Algebra

Question

Fill in the blank with \(<,=\), or \(>\). 44 _____ \(-(-44)\)

Step-by-Step Solution

Answer

44 = 44

Step 1: Understanding the Problem

The exercise asks us to compare 44 and (-(-44)) , and fill in the blank with either <, =, or >.

Step 2: Simplify the Second Expression

To compare the numbers, first simplify (-(-44)) . The double negative sign cancels each other out, so (-(-44)) becomes 44 .

Step 3: Compare the Numbers

Now compare the simplified expression with 44 from the left side of the inequality: 44 and 44 . Since both are equal, the correct comparison is 44 = 44 .

Key Concepts

Inequality Symbols

In mathematics, inequality symbols are crucial when we need to compare two values. They tell us the relationship between two expressions. Here's what each symbol means:

• '<', stands for less than. For example, if we say 3 < 5, it means 3 is less than 5.
• '=', represents equality. It means both values are the same. For example, 5 = 5.
• '>', stands for greater than, meaning the value on the left is larger than the value on the right. For example, 7 > 4.

Understanding these symbols helps us evaluate and decide how to fill in blanks when comparing numbers. In our exercise, since both expressions simplify to the same value, 44, we used the '=' symbol.

Simplifying Expressions

Simplifying expressions means making them easier to understand or compare by reducing them to their most basic form. This often involves combining like terms, performing arithmetic, or canceling out operations like double negatives.

For the expression in our exercise, (-(-44)), the double negative is an important concept. A negative sign in front of a negative number cancels out, transforming (-(-44)) into 44.

This simplification process makes it possible to directly compare or compute expressions without confusion. Always ensure all parts of an expression are fully simplified before making comparisons or solving equations.

Negative Numbers

Negative numbers are numbers less than zero, and they have the '-' sign in front of them. They represent quantities that are opposite to positive numbers, which are greater than zero.

Here are some fundamental points about negative numbers:

• Adding a negative number is like subtracting the absolute value of that number.
• Subtracting a negative number is like adding the absolute value of the negative number. For instance, 7 - (-3) becomes 7 + 3, which equals 10.
• The double negative rule states that when two negative signs are together, they neutralize, becoming a positive. So, -(-a) becomes a.

Understanding how to work with negative numbers is critical for simplifying expressions, like in the exercise where (-(-44)) simplified to 44.