Q3B. - Algebra 1

Question

Determine a valid conclusion that follows from the statement If one number is negative and another is positive, then their product must be negative. If a valid conclusion does not follow, write no valid conclusion and explain why.

The product is 10.

Step-by-Step Solution

Answer

The conclusion does not follows from the statement “If one number is negative and another is positive, then their product must be negative” as it does not say anything about the product of two numbers is positive.

Step 1. Apply the concept of the product of negative and positive.

If one number is negative and another is positive, then their product must be negative.

Step 2. Analyze the data.

Given the product of numbers is 10.

10 is positive.

Step 3. Multiply.

We will reverse the statement “If one number is negative and another is positive, then their product must be negative”. The reverse of the statement is “If the product of two numbers is negative, then one number is negative and another is positive”.

We are given the product is 10, which is positive, so we cannot use the statement or its inverse.

So, the conclusion does not follow from the statement “If one number is negative and another is positive, then their product must be negative” as it does not say anything about the product of two numbers being positive.