how would you write “the next of four times a number” in a math problem 

To write "the next of four times a number" as part of a math problem, you need to transform the verbal expression into a mathematical expression and then create a question around it.

### Mathematical Expression

The expression for "the next of four times a number" is:

\[ 
4x + 1 
\]

Where:
- \( x \) is the variable representing the unknown number.
- \( 4x \) is four times the number.
- Adding 1 makes it "the next of" four times the number.

### Writing a Math Problem

Here's a math problem incorporating this expression:

---

**Problem:**

A number, \( x \), is multiplied by 4, and then 1 is added to the result. If the final result is 21, what is the value of the number?

**Solution:**

Given the expression \( 4x + 1 = 21 \), solve for \( x \):

1. Subtract 1 from both sides:
   \[
   4x = 20
   \]

2. Divide by 4:
   \[
   x = 5
   \]

Thus, the number is \( x = 5 \).

---

### Another Example

You can also write a math problem in a word problem format:

---

**Problem:**

Sara is thinking of a number. She multiplies this number by 4 and then adds 1. If the result is 29, what number is Sara thinking of?

**Solution:**

To find the number, set up the equation:

1. Let \( x \) be the number.
2. Write the equation based on the problem: \( 4x + 1 = 29 \).

Solve for \( x \):

1. Subtract 1 from both sides:
   \[
   4x = 28
   \]

2. Divide by 4:
   \[
   x = 7
   \]

Sara's number is \( x = 7 \).

---

### Explanation

- **Translation:** "The next of four times a number" translates to \(4x + 1\).
- **Setup:** Create a scenario where this expression equals a known value.
- **Solve:** Use algebraic steps to find the unknown number \(x\).

### Questions for Further Exploration

Here are some related questions to deepen your understanding:

1. How would you express "twice a number minus five" in a math problem?
2. Create a math problem involving "three times a number increased by ten equals forty."
3. How can you write a problem with "the product of a number and six is reduced by four to equal twenty"?
4. Formulate a problem using "five times the sum of a number and three equals thirty."
5. Write a problem involving "seven less than twice a number equals fourteen."
6. How can you express "half a number plus nine equals twenty-one" as a math problem?
7. Create a problem with "the square of a number minus two equals thirty."
8. How would you represent "ten more than the cube of a number is fifty" in a math problem?

### Tip

When creating math problems from verbal expressions, always ensure clarity in setting up the equation. Identify the unknown variable, establish relationships, and translate the problem into an algebraic equation.

Learn how to translate 'the next of four times a number' into a mathematical expression, solve related problems, and understand the underlying algebraic concepts. Suitable for Grades 6-8.

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