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Chapter 1: Problem 61

Simplify each expression. $$ 2(4 x+6)+3 $$

Short Answer

Expert verified
8x + 15

Step by step solution

01

- Distribute the 2

Multiply each term inside the parenthesis by 2:\[2(4x + 6) + 3 = 2 \times 4x + 2 \times 6 + 3\]
02

- Simplify multiplication

Carry out the multiplication operations:\[2 \times 4x + 2 \times 6 + 3 = 8x + 12 + 3\]
03

- Combine like terms

Combine the constant terms (12 and 3):\[8x + 12 + 3 = 8x + 15\]

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Key Concepts

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

Distributive Property
When dealing with algebraic expressions, you often encounter situations where you need to apply the distributive property. This property allows you to multiply a single term by each term within a parenthesis. For instance, if you have the expression \(2(4x + 6) + 3\), the distributive property helps you to simplify it.

Here鈥檚 the step-by-step approach:

  • Multiply each term inside the parenthesis by 2: This means you distribute the 2 across both \(4x\) and 6.
  • You get: \(2 \times 4x\) and \(2 \times 6\).

So, \(2(4x + 6) + 3\) becomes \(2 \times 4x + 2 \times 6 + 3\).

By following these steps, you use the distributive property correctly to set up your expression for further simplification.
Combining Like Terms
After you have distributed the terms in your expression, the next important step is to combine like terms.

Like terms are terms that have the same variable raised to the same power. For the expression \(8x + 12 + 3\), the terms \(12\) and \(3\) are constants, meaning they can be combined.

Here鈥檚 how you do it:

  • Identify like terms: In the given expression, \(8x\) is a term with a variable, and \(12\) and \(3\) are constant terms.
  • Combine the constant terms: Add \(12\) and \(3\) together to get \(15\).

So, \(8x + 12 + 3\) simplifies to \(8x + 15\). By combining like terms, you transform your expression into its simplest form.
Basic Algebra
Understanding basic algebra provides the foundation for all higher-level math concepts. Whenever you are working with algebraic expressions, always aim to simplify the expression as much as possible.

To simplify an expression like \(2(4x + 6) + 3\), follow these steps:

  • Apply the distributive property: Distribute the 2 across the terms inside the parenthesis, resulting in \(8x + 12\).
  • Combine like terms: Simplify the expression further by adding the constants \(12\) and \(3\), which gives you \(15\).

The final simplified expression is \(8x + 15\).

Remember, the goal of basic algebra is to make expressions as manageable and understandable as possible through various techniques like distributing and combining terms. Keep practicing to become more confident with these concepts.

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Most popular questions from this chapter

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