Problem 70 Simplify each expression. $$ ... [FREE SOLUTION]

Chapter 0: Problem 70

Simplify each expression. $$ -4|2-4|+8 \cdot 2 $$

Short Answer

Expert verified

Simplified expression: 12

Step by step solution

- Evaluate the Absolute Value

First, evaluate the absolute value expression inside the vertical bars. Calculate then simplify. Replace the absolute value with the result. The expression becomes Calculate the final result. The expression now becomes Calculate the final result. Thus, the simplified expression equals 12. is equal to This is the first step. Perform the multiplication operation after this.. Simplify and complete the calculations. Perform multiplication and subtraction. Finally, add the number. This will give the amplitude.

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Key Concepts

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

Absolute Value

Let鈥檚 start by understanding the absolute value because it is one of the core parts of our exercise. Absolute value refers to the distance a number is from zero on a number line, regardless of direction. It is always a positive number or zero. We use vertical bars to denote absolute value, like this: $ |x| $.In our problem, we see $ |2 - 4| $. To solve this, follow these steps:

Calculate the expression inside the absolute value: $ 2 - 4 = -2 $.
Find the absolute value of $-2$: $ |-2| = 2 $.

After this step, the expression changes from $ -4|2-4| + 8 \cdot 2 $ to $ -4 \cdot 2 + 8 \cdot 2 $. Now let's move to the next concept.

Order of Operations

The order of operations is critical when simplifying expressions in algebra. It tells us the sequence in which to perform operations. The acronym PEMDAS helps remember this order:

Parentheses
Exponents
Multiplication and Division (left to right)
Addition and Subtraction (left to right)

Notice the original exercise expression: $ -4|2-4| + 8 \cdot 2 $. After simplifying $ |2-4| $, our expression became $ -4 \cdot 2 + 8 \cdot 2 $. According to PEMDAS, next we do the multiplication before addition/subtraction.

First, perform the multiplications:

$ -4 \cdot 2 = -8 $
$ 8 \cdot 2 = 16 $

So now, our expression is $ -8 + 16 $. Moving to the final steps, we perform addition/subtraction last: $-8 + 16 = 8$.This is the simplified result!

Multiplication and Addition in Algebra

In the world of algebra, multiplication and addition are fundamental operations. Let鈥檚 dive a little deeper into how these operations work together.Multiplication means scaling one quantity by another. For example, in $ 8 \cdot 2 $, we are scaling 8 by 2, which gives us 16. Addition involves combining quantities. So, in our expression $ -8 + 16 $, we combine these values. When performing these operations, always remember the order of operations to avoid mistakes. In our simplified expression $ -4|2-4| + 8 \cdot 2 $, we first handled the absolute value, then multiplication, and finally addition:

Simplified to $ -4 \cdot 2 + 8 \cdot 2 = -8 + 16 $
Resulting in $ -8 + 16 = 8 $.

Understanding these basics allows us to simplify complex expressions accurately and efficiently.

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91影视

Simplify each expression. $$ -4|2-4|+8 \cdot 2 $$

Short Answer

Step by step solution

- Evaluate the Absolute Value

Key Concepts

Absolute Value

Order of Operations

Multiplication and Addition in Algebra

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