Question

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”?

Answer 1

From the question we have been given an inequality and asked to solve it. For this question we will use interpretation and convert the data given into numerical form. After converting it into numerical form we will use basic mathematical operations like addition, subtraction and division and simplify the equation.

Complete step-by-step solution:
This is mostly interpretation, so, we will do as follows.
We know that eight times a number is $8x$, therefore it’s $8x$.
Minus twenty seven is subtracting $27$, so we get as follows.
$\Rightarrow 8x-27$
“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 will assume it as $x$.
Plus eighteen means …plus $18$. So, we can write it as follows.
$\Rightarrow -x+18$
So, we got the inequality as follows.
$\Rightarrow 8x-27\le -x+18$
To solve this question we will add $27$ on both sides and also add $x$ to both the sides of the inequality.
$\Rightarrow 8x-27\le -x+18$
$\Rightarrow 8x-27+x+27\le -x+18+x+27$
$\Rightarrow 9x\le 45$
Then we will divide both sides by $9$. We get the equation reduced as follows.
$\Rightarrow x\le 5$
Therefore from interpretation, we can say that the answer is $\Rightarrow x\le 5$.

Note: Students must be very careful in doing the calculations. Students should be able to understand the question and must do interpretation very carefully. If you make a mistake like for example if you write $\Rightarrow 8x+27$ instead of $\Rightarrow 8x-27$ then our solution will be wrong.