How do you write an inequality and solve given "eight times a number minus twenty seven is no more than the negative of that number plus eighteen"?

Oct 11, 2017

$8 x - 27 \le - x + 18$
Answer is 5 and all numbers less than that.

Explanation:

This is just mostly interpretation, so to do this, we know 8 times a number is 8x, therefore it's 8x.
Minus twenty-seven is subtracting 27, so $8 x - 27$.
"No more than" means nothing more, but it can be less so $\le$(that means less than or equal to which means the number on the right has to be greater than the number on the left or it can be equal to it).

Negative of that number means $- x$ because we don't know what "that number" is so we can assume it's x.

Plus 18 means...plus 18? So you can do $- x + 18$.

To solve this, you can add 27 on both sides and also add x to both sides to get:
$9 x \le 45$
Then divide both sides by 9 to get $x \le 5$. Therefore from interpretation, you can say that the answer is 5 and all numbers less than that works.