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Chapter 1: Problem 45

In Exercises \(1-72\), compute the value of each expression. $$4-8-6+3$$

Short Answer

Expert verified
-7

Step by step solution

01

Understand the Problem

The task is to compute the value of the expression: $$4 - 8 - 6 + 3.$$ This involves applying basic arithmetic operations.
02

Perform the Subtractions in Order

First, perform the subtraction in the expression from left to right. Start with: $$4 - 8.$$ This equals $$-4.$$ Now, continue with: $$-4 - 6.$$ This equals $$-10.$$
03

Perform the Addition

Finally, add 3 to the resulting value from Step 2. So, $$-10 + 3$$ equals $$-7.$$

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Key Concepts

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

Subtraction
Subtraction is one of the fundamental arithmetic operations. To subtract means to take away from a number. For instance, if you have 4 apples and you give away 2, you are left with 2 apples. Mathematically, this is represented as: 4 - 2 = 2.
In the given exercise, the subtraction steps are as follows:
  • First, we subtract 8 from 4. So, 4 - 8 equals -4.
  • Next, we subtract 6 from the result, -4. Therefore, -4 - 6 equals -10.
Note: Always move from left to right when performing multiple subtractions in a sequence.
Addition
Addition is the process of combining numbers to form a larger number. For instance, if you have 3 apples and you get 2 more, you now have 5 apples. Mathematically, this is represented as: 3 + 2 = 5.
In the given exercise, once we have the result from the subtraction steps, we need to perform one final addition.
  • We add 3 to the number -10 that we got from the previous subtraction. Therefore, -10 + 3 equals -7.
Adding a positive number to a negative number involves moving closer to zero on the number line.
Step-by-Step Computation
Breaking down math problems into smaller steps makes them more manageable. Let's look at the problem again: 4 - 8 - 6 + 3.
Here is the step-by-step process:
  1. First, handle the first subtraction: 4 - 8 = -4.
  2. Next, take the result and perform the next subtraction: -4 - 6 = -10.
  3. Finally, take the result of that subtraction and add 3: -10 + 3 = -7.
By following step-by-step processes, you ensure that you do not miss any operations and arrive at the correct answer efficiently. Remember to work from left to right for both addition and subtraction.

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Most popular questions from this chapter

Evaluate the given expression. Remember to follow the order of operations. $$32+16 \div 8-6$$

Explain how you could use the commutative and/or associative properties to make the following computations easier to do. (a) \(-1.7+12.9-8.3\) (b) 10( 7)\((-2.3)\) (c) \(\frac{-10(3.2)}{-1.6}\) (d) \(-30\left(\frac{1.6}{3}\right)(-10)\)

Sketch the given set on a number line. $$\\{x | 1 \leq x<3\\}$$

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

In Exercises \(1-72\), compute the value of each expression. $$52-(-38)-67$$
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