Match each description to the expression that has the same meaning: 3 less than the product of 8 and a number, 3 more than the difference of 8 and a number, 3 times the difference... Match each description to the expression that has the same meaning: 3 less than the product of 8 and a number, 3 more than the difference of 8 and a number, 3 times the difference of a number and 8, 3 times the sum of number and 8. Read more

Steps to Solve

1. Analyze the first description: "3 less than the product of 8 and a number"

   This means we take the product of 8 and a variable, say $n$. The expression becomes $8n$. Then, to find 3 less than this product, we subtract 3: $$ 8n - 3 $$

2. Analyze the second description: "3 more than the difference of 8 and a number"

   This describes taking the difference of 8 and a variable $n$, which results in $8 - n$. Then, we add 3 to this difference: $$ 3 + (8 - n) $$

3. Analyze the third description: "3 times the difference of a number and 8"

   Here, we take the difference of a variable $n$ and 8, which is $n - 8$. The expression becomes: $$ 3(n - 8) $$

4. Analyze the fourth description: "3 times the sum of a number and 8"

   For this expression, we first find the sum of a variable $n$ and 8, which gives us $n + 8$. Then, we multiply this sum by 3: $$ 3(n + 8) $$

5. Match each description to its expression

   • "3 less than the product of 8 and a number" matches to $8n - 3$.
   • "3 more than the difference of 8 and a number" matches to $3 + (8 - n)$.
   • "3 times the difference of a number and 8" matches to $3(n - 8)$.
   • "3 times the sum of a number and 8" matches to $3(n + 8)$.