Question

The solution of linear inequality $2-x<5$ is
(a) $x>-3$
(b) $x<-3$
(c) $x>3$
(d) $x<3$

Answer 1

To solve the question, we have to know the concept of inequality. Now, if we go through the concept of inequality in mathematics, we come to know that inequality is a relation that makes a non-equal comparison between two numbers or other mathematical expressions. It is also used most often to compare two numbers on the number line by their size.

Complete step-by-step solution:
Before we start the problem we have to know the different inequality symbol like $>$ (greater than),$<$
(Less than),$\ge$ (greater than equal to) and $\le$ (less than equal to). Now take an example so that it will
Polish our concept.
Example:$x+3 >15$
Now we subtract 3 from both sides
$x+3-3 >15-3$
Now we simplify it and we can get
$x> 12$
We have to know some key points of inequality such as if we multiply (or divide) both sides by a negative number and if we are swapping left and right-hand sides, it will change the direction of
Inequality ($''<''$ changes to$''>''$ ).
Now we come to our given problem that is,
$2-x< 5$
Now we subtract 2 from both sides and we will get,
$2-x-2< 5-2$
Now we simplify the expression and we will get,
$-x< 3$
Now we multiply both sides by $-1$ and we will get,
$(-x)(-1)> 3(-1)$
It is called reverse the inequality.
Now we simplify the equation and we can get,
$x> -3$
Hence the correct option is (a)$x >-3$.

Note: Here student must take care of the concept of inequality. Sometimes student did a mistake because they think $''>''$ and $''\ge ''$ is same but there is little difference between greater than $\left( > \right)$ And $\left( \ge \right)$. If we take an example $x>3$, its range is $\left( 3,\infty \right)$. But if we take $x\ge 3$ , its range is $\left[ 3,\infty \right)$.