Problem 94 - Beginning and Intermediate Algebra

Question

Perform each indicated operation. $$ -8-[(-4-1)+(9-2)] $$

Step-by-Step Solution

Answer

\(-10\)

Step 1 - Simplify Inside the Innermost Parentheses

First, simplify the expressions inside the innermost parentheses: \(-4 - 1 = -5\) and \(9 - 2 = 7\).

Step 2 - Combine Results Inside Brackets

Next, add the results from Step 1 inside the brackets: \[-(-5 + 7)\.\]

Step 3 - Perform the Addition Inside Brackets

Now, perform the addition inside the brackets: \(-5 + 7 = 2\), resulting in \(-[2]\).

Step 4 - Apply the Negative Sign Outside the Brackets

Finally, apply the negative sign outside the brackets to the simplified term inside: \(-(2) = -2\). Combine this with \(-8\): \(-8 - 2 = -10\).

Key Concepts

simplifying expressions

Simplifying expressions is the process of breaking down complex mathematical phrases into their simplest forms.This makes problems easier to solve and understand.In the given exercise, we started by addressing the innermost calculations first.
For example, in the expression \(-4 - 1\), we simplified it to get \(-5\).Doing this step-by-step simplification ensures accuracy and clarity in results.
Simplifying expressions generally involves:

• Following the order of operations
• Combining like terms
• Handling any negative numbers carefully

parentheses

Parentheses \( ( ) \) and brackets \[ [ ] \] are used in math to group parts of an expression that need to be solved first.In our exercise, we encounter both types.
It's crucial to solve the innermost parentheses first before handling anything outside.
For example:

• Simplify inside the parentheses \( (-4 - 1)\) to get \(-5\).
• Next, simplify inside the second set of parentheses \( (9 - 2) \), which results in \(7\).

By handling parentheses correctly, we follow the math convention and avoid mistakes.

negative numbers

Negative numbers can be tricky but understanding them is essential.When simplifying expressions with negative numbers, always pay close attention to the sign.
In our exercise, we had several negative numbers like \(-8\) and \(-5\).When we combined \(-5\) and \(7\), we got \(2\) because \( -5 + 7 = 2\).
Finally, when we handled \(-[2]\), it became \(-2\).Key points to remember about negative numbers:

• Adding a negative is like subtracting.
• Subtracting a negative is like adding.
• A negative sign outside parentheses affects everything inside.

addition and subtraction

Addition and subtraction are basic operations but can get complex in larger expressions.
In our problem, we needed to add and subtract within parentheses first.We moved step-by-step to make sure each part was correct.
For instance, after simplifying \(-4 - 1\) and \(9 - 2\), we then combined \(-5 + 7 = 2\).Finally, we handled the subtraction outside the brackets: \(-8 - 2 = -10\).
Key tips:

• Always perform operations inside the parentheses first.
• Follow the order of operations: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction (PEMDAS).
• Double-check your work at each step.