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Chapter 1: Chapter 1

Problem 4

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Evaluate \(2-\\{5+(2-3)+[2-(3-4)]\\}\)

Short Answer

Expert verified
The evaluated expression is \(-5\), found by following the order of operations (PEMDAS/BODMAS) and simplifying the innermost parentheses first, then working outward.
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TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1: Identify and start with the innermost parentheses

In the given expression, identify the innermost parentheses (or brackets) and perform the operation inside those first. Here, the innermost parentheses are \( (2-3) \) and \((3-4)\). First, let's simplify these two parenthetical expressions: \(2 - 3 = -1\) \(3 - 4 = -1\) Now, substitute these values back into the original expression: \(2 - \{5 + (-1) + [2 - (-1)]\}\).

Step 2: Simplify the expression inside the other parentheses

Next, perform the operations inside the other parentheses (or brackets) - in this case, the square brackets [ ]. Continuing with the simplification, we now have: \(2 - \{5 + (-1) + [2 - (-1)]\} = 2 - \{5 + (-1) + [2 + 1]\}\) Now, add 2 and 1 inside the square brackets: \(2 - \{5 + (-1) + 3\}\)

Step 3: Simplify the entire expression inside the curly brackets

Now, perform the operations inside the curly brackets { }. Add and subtract in the order they appear: \(2 - \{5 + (-1) + 3\} = 2 - \{4 + 3\}\) Now, add 4 and 3 inside the curly brackets: \(2 - \{7\}\)

Step 4: Subtract the value in the curly brackets from 2

Finally, subtract the value inside the curly brackets from 2: \(2 - 7 = -5\) So, the evaluated expression is: \(-5\)

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