Problem 79 - Elementary Algebra

Question

Simplify. $$ -(-9) $$

Step-by-Step Solution

Answer

The expression simplifies to 9.

Step 1: Identify the Expression

The given expression is \(-(-9)\). Notice that there is a double negative sign present.

Step 2: Apply the Double Negative Rule

When there are two negatives next to each other, they cancel each other out. Therefore, \(-(-9) = 9\).

Step 3: Verification

To verify, consider how the double negative rule applies: negative of a negative leads to a positive. Thus, the expression \(-(-9)\) simplifies to \(9\).

Key Concepts

Simplification

Simplification makes math expressions easier to understand and work with. It boils down to reducing an expression to its most basic form.

For example, if you have a complex expression like \(-(-9)\), you aim to eliminate unnecessary parts. When performing simplification, you ask yourself: what can be removed or combined in this expression to simplify it further?

In the case of \(-(-9)\), understanding how double negatives work allows you to directly simplify the expression to \(9\). Always make sure to double-check your results by thinking over arithmetic rules, which makes simplification a vital skill in math.

Negative Numbers

Negative numbers can initially be confusing, but they're easier to understand with practice. They are simply numbers that are less than zero and represented with a minus sign.

Think about them like this:

• If you owe someone money, that's a negative financial situation.
• If the temperature drops below zero, that's a negative temperature.

In arithmetic, negative numbers provide a way to perform operations that "reverse" others: subtracting a positive number is like moving backward.

When it comes to double negatives, like \(-(-9)\), familiarity with these rules helps. A negative of a negative returns you to the original positive value: think about negating as switching to the opposite sign.

Algebraic Expressions

Algebraic expressions can seem intimidating, but they are essentially combinations of variables, numbers, and mathematical operations. They are expressions that don't have specific values but instead consist of terms combined thoughtfully.

Here's what's often involved:

• Variables (like \(x\), \(y\))
• Numbers (such as 10, \(-9\))
• Operations (addition, subtraction, etc.)

Algebraic expressions allow for more flexibility in math. They let us solve problems across different scenarios but can also include signed numbers where understanding the rules about negatives is crucial.

So, when simplified, expressions like \(-(-9)\) are easily tackled because you can apply arithmetic rules and simplify to find numeric answers readily.