Answer:
The first thing to do is translate the sentence into mathematical notation.
"no more than" means "less than or equal to" which is written as ≤
"seven less than a number" means we are subtracting 7 from a number. We don't know what the number is, so we can use a variable (like n) for the number. So "seven less than a number" becomes n - 7.
The whole thing becomes 12 ≤ n - 7.
To solve for n, we can add 7 to both sides.
19 ≤ n.
19 is less than or equal to n, which means the smallest (minimum) value of the number is 19.
We could also do it without an inequality:
If 12 is 7 less than a number, then the number is 19, because 19-7=12. If we chose a smaller number, like 18, then 7 less than 18 is smaller than 12, which is not allowed (12 is no more than 7 less than the number). So the smallest possible value of the number is 19.
Let the number be p.
Next, "seven times p" can be written like so:-
[tex]\pmb{7p}[/tex]
This expression is less than 18:-
[tex]\bigstar{\boxed{\pmb{7p < 18}}}[/tex]
Hope everything is clear; if you need any explanation/clarification, kindly let me know, and I will comment and/or edit my answer :)
