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Chapter 1: Problem 70

In Exercises \(67-74,\) evaluate the given expression. $$-10+6 \cdot 3-14$$

Short Answer

Expert verified
-6

Step by step solution

01

- Evaluate the multiplication

First, identify and perform the multiplication operation in the expression: $$6 \times 3 = 18$$ Rewrite the expression with this value: $$-10 + 18 - 14$$
02

- Perform the addition

Next, perform the addition operation: $$-10 + 18 = 8$$ So now the expression becomes: $$8 - 14$$
03

- Perform the subtraction

Finally, perform the subtraction operation: $$8 - 14 = -6$$

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Key Concepts

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

Evaluate Expressions
Evaluating expressions means finding the value of an algebraic expression by performing the operations in the correct order. It is like a step-by-step process to solve a math problem. Understanding the order of operations is crucial because it ensures everyone gets the same answer.
For example, in the expression $$-10 + 6 \times 3 - 14$$,
each operation needs to be done in a specific sequence.
Multiplication Before Addition
When evaluating expressions, always do the multiplication and division before moving on to addition and subtraction. This rule is part of PEMDAS/BODMAS:
  • P/B: Parentheses/Brackets
  • E/O: Exponents/Orders
  • MD: Multiplication and Division (left to right)
  • AS: Addition and Subtraction (left to right)
In our example:
$$-10 + 6 \times 3 - 14$$
First, identify and perform the multiplication:
$$6 \times 3 = 18$$
Rewrite the expression:
$$-10 + 18 - 14$$
This shows that you must handle the multiplication before doing addition or subtraction.
Addition and Subtraction
After completing the multiplication or division steps, you can move on to addition and subtraction. These should be done from left to right as they appear in the expression.
In our example:
$$-10 + 18 - 14$$
First, add $$-10 + 18$$, which is $$8$$
Then, subtract $$14$$ from $$8$$ to get
$$8 - 14 = -6$$
Performing operations in the correct order makes sure you get the right answer every time!

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Most popular questions from this chapter

If possible, list three numbers that are members and three numbers that are not members of the given set. If it is not possible, explain why. \(\\{n | n \text { is a rational number but not an integer }\\}\)

Evaluate the given expression. Remember to follow the order of operations. $$\frac{24-4 \cdot 5+8}{2+3 \cdot 6-4 \cdot 2}$$

Evaluate the given expression. Remember to follow the order of operations. $$30-5(4-2)$$

Locate the given number between two successive integers on the number line. For example, if the given number is \(2.6,\) it is located between 2 and 3 on the number line. $$0.24$$

Consider the following statements. If the statement is true, explain why. If the statement is false, explain why and/or give an example illustrating why. (a) Every rational number is an integer. (b) Every integer is a rational number. (c) \(-15\) is greater than \(-10\) (d) The absolute value of \(-15\) is greater than the absolute value of \(-10 .\) (e) A rational number must be positive. (f) An integer must be positive. (g) Every real number is a rational number. (h) Every rational number is a real number.
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