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Chapter 3: Problem 412

In the following exercises, simplify each expression. $$ 10+4(-3+7) $$

Short Answer

Expert verified
The simplified expression is 26.

Step by step solution

01

Evaluate the Expression Inside the Parentheses

First, solve the expression inside the parentheses. Calculate \(-3 + 7\).
02

Subtract and Add

After solving inside the parentheses, you get:\(-3 + 7 = 4\). Replace the parentheses with this result: \(10 + 4 \times 4\).
03

Multiply

Next, perform the multiplication: \(4 \times 4 = 16\). Replace this multiplication in the expression: \(10 + 16\).
04

Add

Finally, add the terms together: \(10 + 16 = 26\).

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Key Concepts

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

Order of Operations
When simplifying mathematical expressions, it鈥檚 essential to follow the correct order of operations, often remembered by the acronym PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). By following these rules, you ensure that you solve each part of the expression in the right sequence.

For example, in the expression \(10 + 4(-3 + 7)\), you start by solving the innermost parentheses first, before moving on to multiplication and addition.

Not following the correct order can result in incorrect answers. Always make sure to solve each component step by step.
Parentheses
Parentheses indicate that the operations within them should be performed first. They act like a spotlight, showing you the part of the expression that demands your immediate attention.

In our problem \(10 + 4(-3 + 7)\), you first solve what's inside the parentheses: \[-3 + 7 = 4\]. Only after that can you move on to other operations.

Sometimes, you may encounter nested parentheses (parentheses within parentheses). Always start with the innermost set and work outward.
Basic Arithmetic
Basic arithmetic involves the fundamental mathematical operations: addition, subtraction, multiplication, and division. These form the building blocks for all mathematics.

In our example, you鈥檙e required to perform several basic arithmetic operations like addition, subtraction, and multiplication to simplify the expression step by step.

Here are the steps:
  • First, evaluate inside the parentheses: \(-3 + 7 = 4\).
  • Next, perform the multiplication: \(4 \times 4 = 16\).
  • Finally, complete the addition: \(10 + 16 = 26\).
Each step logically follows from the last, confirming the importance of understanding and correctly applying basic arithmetic.

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Most popular questions from this chapter

In the following exercises, multiply. $$ -9 \cdot 4 $$

In the following exercises, solve. $$ -9 r=-54 $$

In the following exercises, model the following to find the sum. $$ 3+7 $$

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