Problem 33 - Elementary Algebra

Question

Rewrite the problem in a simpler form. $$ -(-9) $$

Step-by-Step Solution

Answer

Question: Simplify the expression $$-(-9)$$. Answer: The simplified expression is $$9$$.

Step 1: Interpret the expression

The given expression, $$-(-9)$$, can be interpreted as the negative of negative 9.

Step 2: Simplify the expression

When we have two negative signs attached to each other, they cancel each other out and become a positive. So, the expression $$-(-9)$$ becomes: $$+9$$

Step 3: Final answer

The simplified form of the given expression is $$+9$$, which is simply $$9$$.

Key Concepts

Negative Numbers

Negative numbers are numbers that are less than zero. They are typically represented with a minus sign (−). In mathematics, negative numbers are used to describe values that are below a defined reference point, like a temperature below freezing or a financial loss. They have some unique properties:

• When two negative signs are placed together, as in the expression \(-(-a)\), they cancel each other out. This is because a negative times a negative results in a positive.
• Negative numbers help in representing values in opposite directions; for example, moving backwards or decreasing a debt.

Understanding how to work with negative numbers is crucial in algebra and helps in solving various real-world problems.

Simplification

Simplification is the process of rewriting an expression in a cleaner, more straightforward manner. The goal is often to make an expression easier to read and understand, especially when solving equations. In the case of integer operations:

• When simplifying \(-(-9)\), it becomes \(+9\), because two negatives together make a positive.
• Simplification often involves combining like terms or using arithmetic rules like the one above to reduce the complexity of expressions.
• Always perform simplification step by step to ensure accuracy, moving from more complex expressions to simpler forms incrementally.

By mastering simplification, you can solve mathematical problems more efficiently.

Algebraic Expressions

Algebraic expressions are combinations of variables, numbers, and operations. They form the backbone of algebraic problem-solving. These expressions can be simplified or manipulated using various rules:

• Variables in algebraic expressions can stand for numbers and are often represented by letters such as x, y, or z.
• Operations include addition, subtraction, multiplication, and division, as well as more complex functions and powers.
• When you identify patterns, such as the negative sign rule, you can rewrite expressions into their simplest form to ease understanding and computation.

Working with algebraic expressions requires logical thinking and practice. The skills you develop here are essential for solving equations and understanding more advanced mathematics.