how would you write the next of four times a number

When translating the phrase "four times a number" into mathematical notation, it is represented as \(4x\), where \(x\) stands for the unknown number. The phrase "the next of four times a number" implies adding 1 to this expression, which translates to:

\[ 4x + 1 \]

Here's a step-by-step breakdown of the translation:

1. **Identify "four times a number":** This means multiplying an unknown number (often represented by a variable such as \(x\)) by 4. Mathematically, this is written as \(4x\).

2. **Interpret "the next of":** In mathematical terms, "the next of" typically indicates increasing the expression by 1. So, you add 1 to the expression \(4x\).

3. **Combine the two parts:** The full expression becomes \(4x + 1\).

### Explanation

- **\(x\)**: Represents the unknown number.
- **\(4x\)**: Means four times the number \(x\).
- **\(4x + 1\)**: Signifies the next integer after four times the number, effectively increasing the result by 1.

### Example

Let's take an example where \(x = 3\):

- **Four times the number**: \(4 \times 3 = 12\).
- **Next of four times the number**: \(12 + 1 = 13\).

Therefore, the expression \(4x + 1\) for \(x = 3\) evaluates to 13.

### Questions for Further Exploration

Here are some related questions to expand your understanding:

1. What would be the expression for "twice a number plus three"?
2. How do you express "the square of a number decreased by five"?
3. What is the algebraic expression for "three more than twice a number"?
4. How do you write "five times the sum of a number and four"?
5. How can you represent "seven less than twice a number" mathematically?
6. If "a number is decreased by eight and then multiplied by six," what is the expression?
7. What is the expression for "half of a number increased by nine"?
8. How do you interpret "ten added to the product of three and a number"?

### Tip

To convert verbal expressions into algebraic expressions, identify keywords such as "times," "sum," "product," "difference," and "more than" to guide the formulation of mathematical expressions. Recognizing these keywords is crucial for accurate translation.

Learn how to translate and solve mathematical expressions involving 'four times a number' and 'the next of four times a number'. This detailed explanation covers algebraic expressions and their interpretations, suitable for students in Grades 6-8.

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