Question

Seven more than a number is less than 18

Answer 1

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.

Answer 2

hello!

Let the number be p.

Next, "seven times p" can be written like so:-

`\pmb{7p}`

This expression is less than 18:-

`\bigstar{\boxed{\pmb{7p < 18}}}`

note:-

Hope everything is clear; if you need any explanation/clarification, kindly let me know, and I will comment and/or edit my answer :)