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Chapter 1: Problem 63

\(3(2 x+1)-(4 x-9)\)

Short Answer

Expert verified
2x + 12

Step by step solution

01

- Distribute the 3

Multiply 3 by each term inside the parenthesis: 3(2x + 1) = 6x + 3
02

- Distribute the negative sign

Subtract each term inside the second parenthesis by breaking it into subtraction: -(4x - 9) = -4x + 9
03

- Combine like terms

Add the distributed results from steps 1 and 2 together and combine the like terms: (6x + 3) + (-4x + 9) = 6x - 4x + 3 + 9 = 2x + 12

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Key Concepts

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

distribution property
The distribution property is a useful algebraic rule. It allows you to break down and simplify expressions with parentheses. In this property, you multiply each term inside the parentheses by a factor outside them. For example, in our exercise 3(2x + 1), you multiply 3 by both 2x and 1. This step is shown as:

3 * 2x + 3 * 1 = 6x + 3.

Remember to distribute the factor to all terms inside the parentheses.
combining like terms
Combining like terms is essential in simplification. Like terms are terms that have the same variable raised to the same power. In the example, after distributing, we had 6x from the first parentheses and -4x from the second parentheses.

When we combine 6x and -4x, we focus only on the coefficients (the numbers in front of x).

So, 6x - 4x = (6-4)x = 2x.

Similarly, we combine constants (numbers without variables). Here, 3 + 9 = 12. Adding these two results together gives 2x + 12.
algebraic simplification
Algebraic simplification is reducing expressions to their simplest form. The steps involve distributing factors, combining like terms, and removing unnecessary parentheses. By simplifying, you get cleaner, more understandable expressions.

In our example, we started with a fairly complex expression: 3(2x + 1) - (4x - 9). After distributing and combining like terms, we simplified it to 2x + 12.

This final expression is much simpler and easier to work with in further calculations.
negative sign distribution
Negative sign distribution is crucial when dealing with subtracting expressions. A negative sign in front of parentheses changes the signs of each term inside. For example, in the expression -(4x - 9), the negative sign affects both 4x and -9.

This changes the expression to -4x + 9.

Keep in mind that distributing a negative sign is like multiplying by -1.

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Most popular questions from this chapter

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