Question

How do you write an inequality and solve given “twice a number is more than the sum of that number and 9”?

Answer 1

Hint: Inequality is a statement of an order relationship - greater than or equal to, less than, or less than or equal to between two number or algebraic expressions. Many simple inequalities can be solved by adding, subtracting, multiplying or dividing both sides until you are left with the variable on its own. But these things will change the direction of inequality. In this problem we asked to find the inequality equation as per given statements.

Complete step-by-step solution:
First let us consider the number as variable $n$
We split into two conditions and then we make inequality to both the condition
‘According to the condition (1) twice a number means 2 multiply by the number
That is, $2n$
Then by according to the condition (2) the sum of that number and 9 means we need to add 9 to that number
That is, $(n + 9)$
Now comparing both the condition “twice a number is more than to the sum of that number and 9”
The first condition is bigger so we write as
$2n > (n + 9)$
Now subtract $n$on both sides of the inequality,
$2n - n > n + 9 - n$
$n > 9$
Thus the inequality equation obtained

Hence we get the required answer $n > 9$

Note: Inequality symbols are $ \ne $ not equal to, $ > $ greater than, $ < $ less than, $ \geqslant $ greater than or equal to, $ \leqslant $ less than or equal to. By using this we solve the inequality equations. This kind of problem has to be solved by making algebraic expressions because the question is given in statements. So that the problem is solvable by basic mathematical operations on comparing inequalities.