Problem 87 Perform each indicated operation... [FREE SOLUTION]

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Chapter 1: Problem 87

Perform each indicated operation. $$ -3+[(-5-8)-(-6+2)] $$

Short Answer

Expert verified

These operations are simplified to 21

Step by step solution

Identify and simplify inner expressions

First, identify and simplify the expressions inside the brackets. Start by simplifying

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

order of operations

When performing algebraic operations, it's essential to follow the order of operations to get the correct result.
The remembered acronym PEMDAS stands for Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
Always start with operations inside parentheses or brackets.
Then, handle exponents (if any).
Next, move on to multiplication or division as they come from left to right.
Finally, perform addition or subtraction from left to right.
For our exercise, we follow these steps:
1. Simplify expressions inside the brackets, then
2. Perform addition and subtraction outside the brackets.

negative numbers

Dealing with negative numbers can sometimes be confusing, but once you understand the rules, it gets easier.
When subtracting negative numbers, it's the same as adding their positive counterpart.
For example, \-(-6) \ equals \ 6. Similarly,
adding two negative numbers means you are moving further left on the number line.
For instance, \-5 - 8 \ equals \ -13.
In our exercise, an essential point to remember is when subtracting $ -6 + 2 $ inside the bracket;
it simplifies to \ 4 since you're subtracting a positive result, which is \ 4.

brackets in algebra

Brackets in algebra are used to indicate the terms or expressions that should be simplified first.
They organize operations, showing which actions to perform together.
In our example, first focus on simplifying the expressions inside all brackets:

Start with the innermost bracket expression $ -5 - 8 $. This simplifies to \ -13.
Then move to the other bracket expression $ -(-6 + 2) $, which simplifies by calculating $ 6 - 2 = 4 $.

Once these inner expressions are simplified, the brackets can be removed to complete the outer operations.
This way, \ (-5 - 8) - (-6 + 2) \ becomes \ -13 - 4 \ which equals \ -17

Finally, adding the outer part of the expression, \ -3 + (-17) \, results in \ -20.

Always ensure all brackets are resolved before moving to the next part of the expression.

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91影视

Perform each indicated operation. $$ -3+[(-5-8)-(-6+2)] $$

Short Answer

Step by step solution

Identify and simplify inner expressions

Key Concepts

order of operations

negative numbers

brackets in algebra

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