Sure! Let's break down the statement step by step:
1. Identify the unknown quantity: We are told to let [tex]\( x \)[/tex] represent the unknown quantity.
2. Form the product of the number and -6: The statement tells us to find the product of the unknown quantity [tex]\( x \)[/tex] and -6. Mathematically, this is represented as:
[tex]\[
-6 \times x \quad \text{or} \quad -6x
\][/tex]
3. Decrease the product by 7: Next, we need to decrease this product by 7. This means we subtract 7 from the product we found in step 2. Mathematically, this can be written as:
[tex]\[
-6x - 7
\][/tex]
So, the algebraic expression for "The product of a number and -6 decreased by 7" is:
[tex]\[
\boxed{-6x - 7}
\][/tex]
