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Chapter 1: Problem 12

Simplify. Show your steps. $$43-2(2+4)$$

Short Answer

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Question: Simplify the expression: \(43 - 2(2+4)\) Answer: 31

Step by step solution

01

1. Calculate the value inside the parentheses

First, we need to simplify the expression inside the parentheses: \((2+4)\). Since \(2 + 4 = 6\), the expression becomes: $$43 - 2(6)$$
02

2. Perform the multiplication

Now that we've simplified the expression inside the parentheses, we need to perform the multiplication operation: \(2 \times 6 = 12\). The expression simplifies to: $$43 - 12$$
03

3. Perform the subtraction

Finally, we need to perform the subtraction operation: \(43 - 12 = 31\). Therefore, the simplified expression is: $$31$$

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Key Concepts

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

Understanding Parentheses Simplification
When dealing with expressions that include parentheses, it's essential to simplify this part first. Parentheses group parts of an expression that need to be calculated as a single unit before moving on to other operations. They serve as a way of prioritizing mathematical operations.
  • Start by looking inside the parentheses.
  • Identify operations within the parentheses and solve them.
  • If multiple operations are inside, follow the order of operations: parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right), often remembered by the acronym PEMDAS.
In our exercise, the expression inside the parentheses is \(2+4\). With only addition involved, we simply add: \(2+4=6\). The rest of the expression remains unchanged until this calculation is completed.
Mastering Multiplication in Expressions
Once the parentheses are simplified, the next step is often to tackle multiplication. This operation is performed before any addition or subtraction outside of parentheses, according to the order of operations:
  • Identify the numbers to be multiplied. These are often next to the parentheses after they have been simplified.
  • Perform the multiplication, careful to include any sign in front of the number you are multiplying by.
  • Write down the result, replacing the original multiplication in the equation.
For example, after simplifying the expression \(43-2(2+4)\) to \(43-2(6)\), the next step is to multiply \(2 \times 6\), resulting in 12. Replacing this into the expression gives us \(43-12\).
Breaking Down Subtraction
Subtraction is usually the last step when simplifying an expression, especially when dealing with expressions with parentheses and multiplication:
  • After simplifying and performing any required multiplications, move on to subtraction.
  • Line up the numbers carefully to ensure accuracy, particularly in larger calculations.
  • Subtract the smaller number from the larger one, or, if following algebraic rules, maintain the correct flow of operation to respect the sign involved.
In our example, once multiplication to achieve \(43 - 12\) is done, we subtract 12 from 43. This is straightforward and will conclude with a result of 31, providing the final simplified expression.

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