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Chapter 3: Problem 47

Evaluate each of the following: $$-6+3(-9)$$

Short Answer

Expert verified
-33

Step by step solution

01

Distribute the multiplication

First, distribute the multiplication inside the parentheses: 3 multiplied by -9 is -27.
02

Calculate the distribution result

Now rewrite the expression with the distributed value: -6 + (-27).
03

Solve the addition

Finally, add the two numbers: -6 + (-27) = -33.

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Key Concepts

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

Integer Operations
Understanding integer operations is crucial in elementary algebra. Integers include positive and negative whole numbers, as well as zero. Here are some key points to keep in mind:
  • Positive numbers are greater than zero (e.g., 1, 2, 3).
  • Negative numbers are less than zero (e.g., -1, -2, -3).
  • Zero is neutral; it is neither positive nor negative.
When performing operations on integers, such as addition, subtraction, multiplication, and division, it is essential to follow specific rules. For example, when you multiply or divide two integers with the same sign, the result is positive. Conversely, when the signs are different, the outcome is negative. Recognizing these rules will significantly help you work through algebraic expressions like -6 + 3(-9).
Distributive Property
The distributive property is an important algebraic rule that helps simplify expressions and perform calculations more easily. It allows you to distribute a factor across terms inside parentheses. Mathematically, the distributive property is expressed as:
\(a(b + c) = ab + ac\)
In the exercise -6 + 3(-9), the distributive property is used as follows:
  • First, distribute the 3 to each term inside the parentheses (in this case, just -9).
  • This results in 3 * -9, which equals -27.
Now, -6 + 3(-9) becomes -6 + (-27). This simplification makes it easier to perform the next operation, which is to add the integers together.
Addition of Negative Numbers
Adding negative numbers can be tricky, but understanding a few core principles will help you navigate through such problems. Here are some guidelines:
  • Adding a negative number is the same as subtracting its positive counterpart. For example, adding -5 is the same as subtracting 5.
  • When you add two negative numbers, the result is always more negative.
In the provided exercise -6 + (-27), you are essentially combining two negative numbers. Think of it as moving further left on the number line:
  • Start at -6, and then move 27 units further left.
  • This gets you to -33.
Thus, -6 + (-27) equals -33, bringing us to the final solution. By understanding these principles, you can confidently tackle similar problems in elementary algebra.

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Most popular questions from this chapter

A secretary and a trainee are processing a pile of 124 forms. The secretary processes 15 forms per hour, and the trainee processes 7 forms per hour. If the trainee begins working at 9: 00 A.M. and is then joined by the secretary 2 hours later, at what time will they finish the pile of forms?

Set up an inequality and solve it. Be sure to clearly label what the variable represents. An aide in the mathematics department office gets paid \(\$ 3\) per hour for clerical work and \(\$ 8\) per hour for tutoring. If she wants to work a total of 20 hours and earn at least \(\$ 135,\) what is the maximum number of hours she can spend on clerical work?

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Translate the given phrase or sentence algebraically. 7 greater than \(x\)

Perform the indicated operations on the given inequality. Sketch the resulting inequality on a number line. \(-x<-3 ;\) divide each side by \(-1\)
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