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Chapter 7: Problem 139

In the following exercises, simplify using the distributive property. $$11(n-7)-5(n-1)$$

Short Answer

Expert verified
6n - 72

Step by step solution

01

- Apply the Distributive Property

Start by applying the distributive property to both terms in the expression. This means you'll multiply each term inside the parentheses by the number outside: o For the term \(11(n-7)\): \(11 \times n - 11 \times 7\) o For the term \(-5(n-1)\): \(-5 \times n + -5 \times 1\) Combine these results to get: \(11n - 77 - 5n + 5\)
02

- Combine Like Terms

Next, combine the like terms by grouping the terms with \(n\) together and the constant terms together: \(11n - 5n - 77 + 5\)
03

- Simplify the Expression

Simplify the expression by performing the arithmetic operations: \(11n - 5n = 6n\) \(-77 + 5 = -72\) So, the simplified expression is: \(6n - 72\)

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Key Concepts

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

Simplifying Expressions
Simplifying expressions is an essential skill in algebra. It involves reducing a complex expression into a simpler form. This process often includes removing parentheses through the distributive property and combining like terms.
When you simplify an expression, you make it easier to understand and solve. The goal is to combine all possible like terms and eliminate any unnecessary operations. This streamlined form is more manageable for solving equations or further algebraic manipulation. Remember, the fewer the terms, the better!
Combining Like Terms
Combining like terms is crucial in simplifying expressions. Like terms are terms that have the same variable raised to the same power. For example, in the expression from the exercise, you have:
  • 11n and -5n
  • -77 and 5
To combine like terms, you group and add or subtract them accordingly. For instance, with the terms 11n and -5n, you can combine them as follows:
11n - 5n = 6n
Similarly, combine the constants:-77 + 5 = -72. By doing this, it helps to reduce the expression to its simplest form, which in this case is 6n - 72.
Prealgebra Operations
Prealgebra is the foundation for all future algebra courses. It covers basic arithmetic operations like addition, subtraction, multiplication, and division. More importantly, it introduces algebraic concepts such as the distributive property.
The distributive property allows you to multiply a single term by each term inside a set of parentheses. For example, in the expression: 11(n - 7) - 5(n - 1), you use the distributive property as follows:
11(n - 7) = 11n - 77
And for the second part:
-5(n - 1) = -5n + 5.Understanding basic operations in prealgebra helps you handle more complex algebraic expressions and equations more confidently as you progress in your math journey.

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Most popular questions from this chapter

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