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Chapter 1: Problem 290

Simplify each expression. $$ 23-2(4-6) $$

Short Answer

Expert verified
The simplified expression is 27.

Step by step solution

01

Evaluate inside the brackets

First, solve the expression inside the brackets: \(4 - 6 = -2\)
02

Multiply

Next, multiply the result by -2: \(-2 \times -2 = 4\)
03

Simplify the expression

Finally, add the result to 23: \(23 + 4 = 27\)

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Key Concepts

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

Order of Operations
The first essential concept is the order of operations. This tells us in which order we should perform different mathematical actions.
The universally accepted rule is PEMDAS (or BIDMAS).
  • P/B: Parentheses or Brackets
  • E/I: Exponents or Indices
  • MD/DM: Multiplication and Division (left to right)
  • AS: Addition and Subtraction (left to right)
Following these steps ensures that we correctly solve any mathematical expression. In our example:
First, evaluate the expression inside the brackets: \(4 - 6 = -2\).
Next, multiply \(-2\) by \(-2\). Finally, add the result to \(23\).
Distributive Property
The distributive property helps in spreading out terms over addition or subtraction.
It states that \(a(b + c) = ab + ac\). This property simplifies expressions and solves equations.
In tighter steps:
  • Identify the need for distribution: You often encounter the distributive property with parentheses containing a sum or difference.
  • Multiply through: Multiply the term outside the parentheses by each term inside.
  • Combine like terms: Sum similar terms to simplify further.
In our exercise: We had to apply the distributive property in another form. We distribute by multiplying \(-2\) by each term in the bracket.\(-2\times(4-6)\) translates to \(-2\times-2=4\).
Basic Arithmetic
Basic arithmetic covers addition, subtraction, multiplication, and division.
Mastery of these operations is the foundation of solving any algebraic expression.
  • Addition: Combining two numbers or more to get a total.
  • Subtraction: Finding the difference between numbers by 'taking away'.
  • Multiplication: Adding a number to itself a specified number of times.
  • Division: Splitting a number into equal parts or groups.
In the exercise, we used these basic arithmetic operations several times.
First, subtraction inside the brackets: \(4 - 6 = -2\). Then, multiplication: \(-2 \times -2 = 4\). Finally, we used addition: \(23 + 4 = 27\). Combining these operations helps in deriving the correct solution.

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