Question

Solve the following linear inequation in R.
$x + 5 > 4x - 10$

Answer 1

Hint: Start by making the inequality uniform by gathering all the variables to one side and all the constants to the other side. After this is solved for the value of x , we would receive a value which would be either greater or lesser than x, representing the final answer in the form of a set of real numbers.

Complete step by step answer:
Given inequality is:
$x + 5 > 4x - 10$
We see that there is an unbalanced or non-uniform distribution of variables and constants. Therefore, we will try to make it uniform by gathering all the variables and constants to separate sides.
$x + 5 > 4x - 10$
Adding (10-x) to both the sides, we get
$
  x + 5 - x + 10 > 4x - 10 - x + 10 \\
   \Rightarrow 5 + 10 > 3x \\
   \Rightarrow 15 > 3x \\
   \Rightarrow \dfrac{{15}}{3} > x \\
   \Rightarrow x < 5 \\
$
which means x is less than five.
Hence the solution of given inequality will be $( - \infty ,5)$.
We have kept the small brackets also known as open brackets as x did not equal to 5 , meaning x can be close to 5 but always less than 5.


Note:
Such similar questions can be solved using the same method of adding or multiplying with terms in order to collect all variables and constants at a place. Attention must be given while multiplying with negative sign or negative term as the inequality reverses in this condition.