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Chapter 1: Problem 12

Evaluate each expression. $$-5(6+[(5-7)-4])$$

Short Answer

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Step by step solution

01

Simplify Inside the Parentheses

Start by focusing on the innermost parentheses. The expression is \[(5-7)-4\]. First, calculate \(5 - 7\).
02

Evaluate Innermost Operation

Calculate \(5 - 7\) to get \(-2\). Substitute this back into the expression: \[-5(6+[(-2)-4])\].
03

Simplify Inside the Brackets

Next, evaluate the expression inside the square brackets: \((-2) - 4\). Calculate this to get \(-6\). Substitute this result back into the expression: \[-5(6+(-6))\].
04

Simplify Inside the Parentheses

Now, simplify inside the parentheses: \(6 + (-6)\). Calculate this to get \[0\]. Substitute this back into the expression: \[-5(0)\].
05

Multiply

Finally, multiply the remaining terms: \[-5 \times 0 = 0\].

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Key Concepts

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

Order of Operations
When solving algebraic expressions, it is essential to use the correct order of operations. This ensures you get the right answer every time. The order of operations is often remembered by the acronym PEMDAS:
  • P: Parentheses
  • E: Exponents
  • M: Multiplication
  • D: Division
  • A: Addition
  • S: Subtraction
In this exercise, we begin solving the expression \( -5(6+[(5-7)-4]) \) with the innermost parentheses first, according to PEMDAS. We simplify inside the parentheses and brackets before doing multiplication. Following these steps ensures we simplify correctly at each stage.
Nested Expressions
Nested expressions refer to expressions inside other expressions. They are like layers or 'nesting dolls' within mathematics. In the problem \( -5(6+[(5-7)-4]) \), there are multiple layers of parentheses. The sequence for simplifying nested expressions is to start with the innermost layer and work outward. For instance, we first solve \( 5 - 7 \), then use that result in \( (5 - 7) - 4 \). Then we simplify what's inside the square brackets and finally handle the parentheses. This process ensures we simplify the expression correctly step by step.
Simplifying Algebraic Expressions
Simplifying algebraic expressions involves making them as simple as possible. This typically means reducing the expression down to a single number or a simpler form. In our problem with several steps:
  • First, we resolved \( 5 - 7 \) to get \( -2 \).
  • Next, we substituted \( -2 \) into \((5-7)-4\), getting \( -6 \).
  • Then, inside the parentheses, we added \6\ and \-6\ to get \0 \.
  • Finally, we multiplied \-5\ by \0\ to simplify it to \0 \.
Simplifying algebraic expressions step by step helps avoid mistakes, ensuring accuracy.

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Most popular questions from this chapter

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