Problem 50 Simplify. $$ -(-9)-14+(-23) ... [FREE SOLUTION]

Chapter 2: Problem 50

Simplify. $$ -(-9)-14+(-23) $$

Short Answer

Expert verified

The simplified expression is -28.

Step by step solution

Simplify Double Negatives

The expression begins with twice a negative sign: \[ -(-9) \]A negative sign in front of another negative sign turns the number positive. So, we simplify it as:\[ -(-9) = +9 \]

Substitute and Rewrite the Expression

Substitute $+9$ back into the original expression. Rewrite the expression:\[ 9 - 14 + (-23) \]

Simplify Addition and Subtraction

First, handle the subtraction:\[ 9 - 14 = -5 \]Then, handle the addition of a negative:\[ -5 + (-23) = -5 - 23 = -28 \]

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Key Concepts

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

Double Negatives

In mathematics, dealing with double negatives can often be a source of confusion, but it's simpler than it seems. Double negatives occur when you have a negative sign in front of another negative sign, like this: $-(-a)$. When you encounter double negatives, the rule is straightforward: two negatives make a positive. Essentially, think of it like removing a debt. If you owe money (negative), and that debt is canceled (another negative), you are effectively gaining money (positive). Thus, when you see $-(-9)$, it simplifies to $+9$. This concept is crucial as it lays a fundamental understanding for solving prealgebra problems efficiently.

Subtraction in Prealgebra

Subtraction in prealgebra involves taking one number away from another. At times, subtraction can look tricky, especially when it interacts with negative numbers. When subtracting, think of it as moving left on the number line. For instance, in the expression $9 - 14$, you start at 9 on the number line and move 14 spaces to the left, resulting in -5. It's important to remember that subtraction can be represented by adding a negative number. This concept ties closely with the operations of addition and subtraction, forming the backbone of solving more complex equations in algebra. By mastering subtraction, students can better navigate and simplify expressions correctly.

Addition with Negative Numbers

Adding negative numbers can seem a bit tricky at first but follows a simple logic. When you add a negative number, it's like subtracting a positive number. Consider the expression $-5 + (-23)$, it's the same as saying $-5 - 23$. You can think of this operation as moving further left on the number line. Starting from -5, moving 23 spaces more in the negative direction, you get -28. A neat trick to keep in mind is adding a negative is equivalent to subtracting the absolute value of that number. Grasping this concept is key in solving algebraic expressions effectively and building a strong foundation in mathematics.

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91影视

Simplify. $$ -(-9)-14+(-23) $$

Short Answer

Step by step solution

Simplify Double Negatives

Substitute and Rewrite the Expression

Simplify Addition and Subtraction

Key Concepts

Double Negatives

Subtraction in Prealgebra

Addition with Negative Numbers

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