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Chapter 15: Problem 50

Simplify. $$ 3-|2-7+4| $$

Short Answer

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Step by step solution

01

Simplify inside the absolute value

First, simplify the expression inside the absolute value. Calculate the values inside the parenthesis: \(2 - 7 + 4\). Subtract and add step-by-step: \(2 - 7 = -5\) \(-5 + 4 = -1\).
02

Evaluate absolute value

Find the absolute value of the result from the previous step. The absolute value of \(-1\) is \(|-1| = 1\).
03

Subtract from 3

Complete the simplification by subtracting the result of the absolute value from 3. \(3 - 1 = 2\).

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Key Concepts

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

Absolute Value
Absolute value gives the distance of a number from zero on the number line, always as a positive value. In other words, the absolute value of a number is always non-negative. For instance, \( |3| = 3 \) and \( |-3| = 3 \). When simplifying expressions involving absolute values, make sure to first resolve the inner expression, then apply the absolute value rule.
Order of Operations
Order of operations is crucial in simplifying expressions. The standard rule to follow is PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). It ensures that everyone solves expressions consistently. For example, in our problem, we must first handle what鈥檚 inside the absolute value before dealing with other operations.
Arithmetic Operations
Arithmetic operations include addition, subtraction, multiplication, and division. They are the building blocks of algebra. In our problem, we performed addition \( (2 + 4) \) and subtraction \( (-7)\) within the absolute value first. Understanding how to correctly perform arithmetic step-by-step is vital in simplifying expressions.
Algebra
Algebra involves using symbols to represent numbers in equations and expressions. Simplifying algebraic expressions involves combining like terms and using fundamental operational rules. In the provided problem, simplifying inside the absolute value and using order of operations are basic yet critical algebraic techniques. They help to methodically break down and solve even complex expressions.

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