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Chapter 0: Problem 89

Use the Distributive Property to remove the parentheses. $$ 6(x+4) $$

Short Answer

Expert verified
6(x + 4) = 6x + 24

Step by step solution

01

- Identify the expression and the terms inside the parentheses

The given expression is \(6(x + 4)\). The terms inside the parentheses are \(x\) and \(4\).
02

- Apply the Distributive Property

The Distributive Property states that \(a(b + c) = ab + ac\). Here, \(a = 6\), \(b = x\), and \(c = 4\).
03

- Multiply 6 by x and 6 by 4

Using the Distributive Property, multiply \(6\) by each term inside the parentheses: \(6 \times x + 6 \times 4\).
04

- Simplify the expression

Calculate the products: \(6 \times x = 6x\) and \(6 \times 4 = 24\), so \(6(x+4) = 6x + 24\).

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Key Concepts

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

Algebra
Algebra is a branch of mathematics that uses symbols, letters, and numbers to represent and solve equations and expressions. These symbols often stand in for unknown values that we aim to determine. One common task in algebra is solving or simplifying expressions. For example, in the exercise given, we deal with the expression and use properties to make it simpler and more manageable.

Algebra helps us understand relationships and patterns. It is foundational for higher mathematics and many real-world applications. By mastering basic algebraic concepts, you will find it easier to tackle more complex mathematical problems in the future.
Simplifying Expressions
Simplifying expressions is a crucial skill in algebra. It involves making an expression easier to understand and work with. To simplify an expression, we manipulate it using various mathematical operations and properties.

In the given example, we simplify the expression using the Distributive Property. Simplifying the expression involves:
  • Identifying the terms inside the parentheses
  • Applying mathematical rules
  • Simplifying the resulting terms
The final simplified form of the expression helps us better understand the problem and makes it easier to use in further calculations or algebraic manipulations.
Multiplication
Multiplication is one of the basic operations in mathematics. It involves adding a number to itself a certain number of times. For example, multiplying 6 by 4 means adding 6 four times: 6 + 6 + 6 + 6 = 24.

In the context of the Distributive Property, we multiply each term inside the parentheses by the number outside. This is what we did in the exercise:
  • 6 was multiplied by x to give 6x
  • 6 was also multiplied by 4 to give 24
This step-by-step multiplication ensures that every term inside the parentheses is appropriately scaled by the number outside, making the overall expression easier to handle.

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Most popular questions from this chapter

Rationalize the denominator of each expression. Assume that all variables are positive when they appear. $$\frac{-3}{\sqrt{5}+4}$$

Expressions that occur in calculus are given. Factor each expression. Express your answer so that only positive exponents occur. $$6(6 x+1)^{1 / 3}(4 x-3)^{3 / 2}+6(6 x+1)^{4 / 3}(4 x-3)^{1 / 2} \quad x \geq \frac{3}{4}$$

Use a calculator to approximate each radical. Round your answer to two decimal places. $$\sqrt{2}$$

Expressions that occur in calculus are given. Factor each expression. Express your answer so that only positive exponents occur. $$4(3 x+5)^{1 / 3}(2 x+3)^{3 / 2}+3(3 x+5)^{4 / 3}(2 x+3)^{1 / 2} \quad x \geq-\frac{3}{2}$$

Simplify each expression. Assume that all variables are positive when they appear. $$6 \sqrt{5}-4 \sqrt{5}$$
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