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Chapter 10: Problem 101

Perform each indicated operation. See Sections 2.1 and 5.4. $$ -3(x+5) $$

Short Answer

Expert verified
-3x - 15

Step by step solution

01

Distribute the Constant

The expression \(-3(x + 5)\) needs to be simplified by distributing the constant \(-3\) to each term inside the parentheses. This means you multiply \(-3\) by \(x\) and by \(5\).
02

Multiply Terms

Calculate the product of \(-3\) and \(x\) to get \(-3x\). Then calculate the product of \(-3\) and \(5\) to get \(-15\).
03

Combine Results

Combine the results from the previous step: \(-3x\) and \(-15\). The simplified expression is given by \(-3x - 15\).

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Key Concepts

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

Algebraic Expressions
Algebraic expressions are combinations of numbers, variables, and arithmetic operations. Understanding them is crucial as they form the basis of many mathematical calculations. The expression in our exercise, \[-3(x + 5)\],consists of a constant (-3), a variable (x),and another constant (5) inside a parentheses.
  • The constant is a fixed numeric value.
  • The variable (x) represents an unknown value that can change.
  • The expression is surrounded by parentheses, signaling that multiplication should occur with the number outside using the distributive property.
When you see an expression like this, remember that you need to follow specific rules to simplify it, such as using the distributive property.
Simplification
Simplification of an expression involves making it as simple as possible without changing its value. It often requires the use of mathematical properties like the distributive property. In the given exercise, we aim to simplify \(-3(x+5)\)by distributing the constant.
The distributive property helps in breaking down expressions into smaller, more manageable parts. You multiply the constant outside the parentheses by each term inside:
  • The first step involves multiplying \(-3\times x\), resulting in \(-3x\).
  • Next, multiply \(-3\times 5\) which gives \(-15\).
Finally, you combine these results to get the simplified expression \(-3x - 15\).
Simplifying expressions is an important skill in algebra, allowing you to rewrite expressions in a more understandable form.
Negative Numbers
Negative numbers are less than zero and are represented with a minus sign. They play a crucial role in mathematics, especially when handling operations like multiplication and division.In our exercise, the number \(-3\)is negative, and understanding how to manage this with other numbers is key to simplifying expressions correctly.
  • When you multiply a negative number by a positive number, the result is negative.
  • This is seen in the step where \(-3\times x\) results in \(-3x\).
  • When \(-3\times 5\) is calculated, it also yields a negative \(-15\).
Working with negative numbers can be tricky, but with practice, you鈥檒l learn how to handle them seamlessly in math operations. Remember, when two negative numbers are multiplied, the result is positive, but in our exercise, all multipliers had mixed signs.

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Most popular questions from this chapter

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