To write and evaluate the expression "three times the difference of nine and a number," we follow these steps:
1. Identify the key terms and replace them with their values:
- "three" is replaced with [tex]\( 3 \)[/tex].
- "times" is represented by multiplication, [tex]\( \times \)[/tex].
- "the difference of" represents subtraction, [tex]\( (- \)[/tex].
- "nine" is replaced with [tex]\( 9 \)[/tex].
- "a number" is represented by [tex]\( h \)[/tex].
2. Construct the mathematical expression:
- "three times" translates to [tex]\( 3 \times \)[/tex].
- "the difference of nine and a number" translates to [tex]\( (9 - h) \)[/tex].
So, the expression in mathematical terms is:
[tex]\[ 3 \times (9 - h) \][/tex]
3. Substitute [tex]\( h = 5 \)[/tex] into the expression:
[tex]\[ 3 \times (9 - 5) \][/tex]
4. Evaluate the expression step-by-step:
- First, calculate the difference inside the parentheses: [tex]\( 9 - 5 = 4 \)[/tex].
- Now multiply the result by [tex]\( 3 \)[/tex]: [tex]\( 3 \times 4 = 12 \)[/tex].
Therefore, the value of the expression when [tex]\( h = 5 \)[/tex] is:
[tex]\[ 12 \][/tex]
The value of the expression when [tex]\( h = 5 \)[/tex] is [tex]\(\boxed{12}\)[/tex].
