Question

How do you write the inequality and solve given “A number decreased by 4 is more than -1”?

Answer 1

Hint: An inequality is an expression whose left-hand side (LHS) and right-hand side (RHS) are separated by one of the following signs \[<,>,\le,\]or \[\ge \]. These signs are called ‘less than’, ‘greater than’, ‘less than or equal to’, and ‘greater than or equal to’ signs respectively.

Complete step by step answer:
We are given the condition that A number decreased by 4 is more than -1. And we have to write an inequality for this condition. We will divide the condition into 3 parts and write the condition for it.
The first part of the condition is A number. This part shows the existence of a number, we do not know the exact number so, assume a variable x which represents this number.
The second part of the condition is: decreased by 4. This part means that the number decreased by 4 or 4 is subtracted from the number which is considered in the first part. We assumed the number to be x, so using the condition till now we got the expression \[x-4\].
The last part of the condition is greater than -1. This part means that all the values we got till now have to be greater than -1. We have to use the \[>\] sign, as this part has the words greater than. From the first two conditions, we get the expression \[x-4\]. from the first two parts of the condition. So, using the last part the inequality can be written as\[x-4>-1\].
Adding 4 to both parts of the above inequality, we get
\[\Rightarrow x-4+4>-1+4\]
\[\Rightarrow x>3\]
So, the inequality for the given condition is written as \[x>3\].

Note:
 These types of problems are not difficult and can be easily solved. But one has to keep attention towards the statement of condition and use appropriate signs according to it. One should not get confused between words like ‘less than’ and ‘less than or equal to’, and use correct signs.