Problem 52 Simplify each of the following e... [FREE SOLUTION]

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Prealgebra

David Arnold

$Math Studyset 91影视 Explanations$ Math

2020 Edition

Chapter 2: Problem 52

Simplify each of the following expressions. $-(-17)$

Short Answer

Expert verified

The simplified expression is 17.

Step by step solution

Understand the Expression

The expression $-(-17)$ has a double negative, meaning two negative signs are attached to the number 17. We need to simplify this expression by addressing the negative signs.

Apply the Rule of Double Negatives

In mathematics, two negative signs next to each other cancel each other out. When you have $-(-x)$, it simplifies to x. Therefore, then$-(-17)$ simplifies to 17.

Write the Simplified Result

Based on the cancellation of the two negative signs, the simplified answer is $ 17 $. Therefore, $-(-17) = 17$ .

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Key Concepts

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

Understanding Double Negatives

In mathematics, double negatives can sometimes cause confusion, but they follow a straightforward rule. When you see two negative signs directly next to each other, they act like mirror images and cancel each other out. This means the double negative changes the sign to positive. To visualize this, imagine walking backwards (negative) and then deciding to walk backwards again (another negative). The effect is the same as moving forward (positive).

Example: If you have the expression $-(-17)$, you are essentially negating the negative sign, turning the number into $ 17 $.
Important Note: Double negatives are not the same as multiplying two negative numbers; they simply negate each other's effect.

Remembering this rule will help make simplifying expressions a breeze!

Recognizing Negative Signs

Negative signs appear frequently in mathematics, and it's crucial to understand their implications. A single negative sign (") flips the sign of a number. In the expression $-17$, the negative sign changes 17 to its negative counterpart. Negative signs can appear in arithmetic, algebra, and various mathematical operations. Be aware of where they appear:

Before numbers, indicating a negative value ( $-3$ means 3 units in the opposite direction of positive).
In subtraction operations, they are seen between numbers (e.g., $ 10 - 7 = 3$, showing a reduction.

Paying close attention to negative signs can change the outcome of calculations and is an essential skill in math.

Simplifying Mathematical Expressions

Simplifying mathematical expressions involves reducing them to their simplest form. This often means removing unnecessary signs or terms. It's like cleaning up a sentence by removing extra words while keeping the meaning intact. Here鈥檚 how to simplify expressions neatly:

Identify and eliminate double negatives: As previously mentioned, $-(-17)$ simplifies to $ 17 $.
Combine like terms: If a problem involves similar terms, add or subtract them to simplify the expression (e.g., $3x + 4x = 7x$).
Apply basic arithmetic operations: Simplify any addition, subtraction, multiplication, or division where possible.

By consistently applying these methods, you'll find mathematics more manageable and can solve problems more efficiently.

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91影视

Simplify each of the following expressions. \(-(-17)\)

Short Answer

Step by step solution

Understand the Expression

Apply the Rule of Double Negatives

Write the Simplified Result

Key Concepts

Understanding Double Negatives

Recognizing Negative Signs

Simplifying Mathematical Expressions

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