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Chapter 0: Problem 69

simplify each algebraic expression. $$ -(-14 x) $$

Short Answer

Expert verified
So the simplified form of -(-14x) is 14x.

Step by step solution

01

Understanding The Double Negative

The given expression is -(-14x). Algebraically, the rule of double negatives states that the product of two negative numbers is always positive. Thus, the two negative signs before the 14x cancels each other out. Hence, the expression -(-14x) becomes +14x, or simply 14x.
02

Writing The Simplified Expression

With the rule of double negatives applied, the simplified form of the expression -(-14x) is 14x.

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Key Concepts

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

Double Negative
In algebra, the concept of a double negative is much like in everyday language. When we see a double negative, it turns into a positive. In the expression \(-(-14x)\), we have two negative signs next to each other. According to the rule of double negatives, these signs cancel each other out. This means we replace the double negative with a single positive. To put it simply, when you apply this rule to \(-(-14x)\), you are left with \(+14x\) or simply \(14x\).

Understanding how double negatives work can help you simplify expressions quickly. Here are some key points to remember:
  • Double negatives make a positive.
  • Two negatives next to each other can be replaced by a positive.
  • This concept is essential for simplifying and solving algebraic expressions.
Algebraic Rules
Algebraic rules are fundamental principles that help in manipulating and simplifying algebraic expressions. These rules guide how operations like addition, subtraction, multiplication, and division are performed with numbers and variables.

In algebra, some key rules are:
  • Combining like terms: Only terms that have identical variables can be added or subtracted.
  • Distribution: Multiplying a number by a group of terms inside parentheses affects each term inside the parentheses separately.
  • Exponents rules: Handling operations that involve powers or exponents require specific calculations.
  • Negative sign handling: Treat negative signs according to whether they are single (resulting in a negative) or double (resulting in a positive).


Knowing and applying these rules correctly simplifies problem-solving and makes understanding complex expressions much easier.
Product of Negative Numbers
The product of negative numbers is an important concept in algebra. When you multiply two negative numbers, the result is positive. This is derived from the rule that the two negatives cancel each other out.

For instance, if you calculate \((-3) \times (-5)\), you would end up with \(15\). The multiplication recognizes each negative sign and cancels them, giving a positive product. This principle is crucial:
  • Multiplying an even number of negative numbers always results in a positive product.
  • Multiplying an odd number of negative numbers results in a negative product.


This rule helps visualize and solve expressions. Remember the cancellation happens because of the algebraic rule that double negatives equate to a positive outcome.

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