The product of three and the sum of a number and two is zero if replaced by 0, true or false

Let's break down the statement to determine if it is true or false.

The statement is:  
"The product of three and the sum of a number and two is zero if replaced by 0."

To understand this, let's restate it mathematically:

If we have a number \( x \), then the sum of the number and two is \( x + 2 \).

The product of three and this sum is \( 3(x + 2) \).

If we are saying that this product equals zero, the mathematical expression is:
\[
3(x + 2) = 0
\]

To solve for \( x \), divide both sides by 3:
\[
x + 2 = 0
\]

Subtract 2 from both sides:
\[
x = -2
\]

So, when \( x = -2 \), the product \( 3(x + 2) \) does indeed equal zero.

**Answer**:  
The statement is **true** because, for \( x = -2 \), the expression \( 3(x + 2) \) equals zero.

Would you like more details or have any other questions?

### Related Questions

1. What happens if the number is different, such as \( x = 0 \)?
2. How would the statement change if it involved a different product, like \( 4(x + 2) = 0 \)?
3. Can you explain why multiplying by zero results in zero?
4. What if the equation was \( 3(x - 2) = 0 \)? What would the solution be?
5. How do you solve for \( x \) if the equation was \( 3(x + 5) = 15 \)?

**Tip**: When you set up an equation, make sure all the terms are correctly placed to match the words of the problem.

Explore how the Zero Product Property applies to equations like 'The product of three and the sum of a number and two is zero if replaced by 0'. Learn how to solve such equations step-by-step with examples and explanations. Suitable for high school students studying algebra.

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