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Let's translate the given phrases into mathematical expressions:

1. **Four times the sum of a number and -5**
   \[
   4(x + (-5)) \quad \text{or} \quad 4(x - 5)
   \]

2. **Nine times a number, decreased by 16**
   \[
   9x - 16
   \]

3. **The product of the sum of \( x \) and \( y \) and the difference of \( x \) and \( y \)**
   \[
   (x + y)(x - y)
   \]

4. **Five less than two times a number is the same as seven**
   \[
   2x - 5 = 7
   \]

5. **If three times a number is increased by 4, the result is -8**
   \[
   3x + 4 = -8
   \]

Would you like more details on any of these translations or have any questions?

Here are five related questions that expand on this topic:
1. How do you solve the equation \(2x - 5 = 7\) for \(x\)?
2. What is the simplified form of the expression \((x + y)(x - y)\)?
3. If \(3x + 4 = -8\), what is the value of \(x\)?
4. How would you translate "the sum of twice a number and three is equal to eight" into a mathematical equation?
5. What are some common mistakes to avoid when translating verbal expressions into mathematical equations?

**Tip:** When translating verbal phrases into mathematical expressions, carefully identify key terms and operations, such as "sum," "product," "increased by," and "decreased by." These keywords help determine the appropriate mathematical operations to use.

Translate the following phrases into mathematical equations:
1. Four times the sum of a number and -5
2. Nine times a number, decreased by 16
3. The product of the sum of x and y and the difference of x and y
4. Five less than two times a number is the same as seven
5. If three times a number is increased by 4, the result is -8

Learn how to translate verbal phrases into algebraic equations with step-by-step solutions. Examples include basic linear equations and operations such as addition, subtraction, multiplication, and the distributive property. Suitable for students in Grades 7-9.

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