Certainly! Let's break down the statement "three times the absolute value of the sum of a number and 6" into a mathematical expression step-by-step:
1. Identify the variable: Let's use [tex]\( n \)[/tex] to represent the unknown number.
2. Find the sum of the number and 6: This can be written as [tex]\( n + 6 \)[/tex].
3. Take the absolute value of the sum: The absolute value of [tex]\( n + 6 \)[/tex] is denoted as [tex]\( |n + 6| \)[/tex].
4. Multiply the absolute value by 3: We then take the absolute value [tex]\( |n + 6| \)[/tex] and multiply it by 3, which gives us [tex]\( 3 \times |n + 6| \)[/tex].
Thus, the expression that represents "three times the absolute value of the sum of a number and 6" is:
[tex]\[ 3 \times |n + 6| \][/tex]
Or more succinctly:
[tex]\[ 3|n + 6| \][/tex]
So, the correct expression is:
[tex]\[ 3|n + 6| \][/tex]
