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Chapter 1: Problem 10

Evaluate each of the following expressions, if possible. $$-(-6-3)$$

Short Answer

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Step by step solution

01

Simplify Inside the Parentheses

First, solve the expression inside the parentheses. Find the result of \(-6 - 3\). Note: When subtracting a positive number from a negative number, you are moving further left on the number line.
02

Solve the Inner Subtraction

Calculate \(-6 - 3\): -3 moves further left on the number line from -6. So, \(-6 - 3 = -9\).
03

Apply the Negative Sign

Simplify the remaining expression which is now: \(-(-9)\). Note: The negative sign outside the parentheses will change the sign of the expression inside the parentheses.
04

Final Calculation

Apply the outer negative sign. The expression becomes \(-(-9) = 9\).

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Key Concepts

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

simplifying parentheses
When working with algebraic expressions, simplifying parentheses is a crucial step. Parentheses indicate which operations should be performed first. For example, in the expression \(-(-6-3)\), you focus on the inner parentheses \(-6-3\) before dealing with the outer negative sign.

Here are some key points to remember when simplifying parentheses:
  • Always perform the operations inside parentheses first.
  • Follow the order of operations (PEMDAS/BODMAS).
  • Be aware of nested parentheses and work from the innermost set outward.
In the given exercise, the first step is to calculate \(-6-3\). Understanding this will make the rest of the calculation straightforward. Once the inner part is simplified, move on to the next step confidently.
negative numbers
Negative numbers can be a bit tricky, but with practice, they'll become easier to handle. In the expression \(-(-6-3)\), negative numbers are involved in both subtraction and negation.

Here are a few tips to master negative numbers:
  • On a number line, moving to the left means subtracting, and moving to the right means adding.
  • Subtracting a positive number from a negative number pushes you further left on the number line.
  • The negative sign outside parentheses changes the sign of everything inside.
For instance, when you calculate \(-6-3\), you're subtracting 3 from -6, moving further left to get \-9\. After that, \(-(-9)\) changes \-9\ to \9\ due to the double negative rule. Remember, two negatives make a positive!
number line operations
Using a number line can help visualize the operations of addition and subtraction, especially with negative numbers. In the exercise \(-(-6-3)\), understanding number line operations can provide clarity.

Here's how number line operations work:
  • Positive numbers move you to the right on the number line.
  • Negative numbers move you to the left on the number line.
  • Subtraction of a positive number moves you left, while addition of a negative number also moves you left.
When calculating \(-6-3\), you start at \-6\ and move three steps to the left, landing on \-9\. Finally, flipping the \-9\ to a \9\ due to the outer negative sign completes the problem. Visualizing these steps on a number line can make the process clearer and simpler.

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Most popular questions from this chapter

Evaluate the given expression. Remember to follow the order of operations. $$48 \div 12 \div 4$$

On a certain day the maximum temperature was \(12^{\circ} \mathrm{C},\) and the minimum temperature was \(-5^{\circ} \mathrm{C} .\) By how many degrees did the temperature vary on this day?

Evaluate the given expression. Remember to follow the order of operations. $$12-4 \cdot 3+6$$

Compute the given expression. Round off your answer to two decimal places where necessary. $$12.4-20(0.8)+4.7$$

In Exercises \(1-72\), compute the value of each expression. $$225-56-97-115$$
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