Question

How do you solve $2n-7>25$ ?

Answer 1

We have been given a linear inequality in one variable. Thus, we shall determine the interval in which variable-n lies so that this inequality holds true. First of all, we shall transpose the constant term from the left hand side to the right hand side of the inequality. Then we shall divide both sides of the inequality to make the coefficient of variable-n equal to 1. Further, we shall write the interval for which this inequality holds true.

Complete step by step solution:
Given that $2n-7>25$.
Firstly we shall transpose the constant term -7 from the left hand side to the right hand side of the equation.
$\Rightarrow 2n>25+7$
$\Rightarrow 2n>32$
Now, we shall divide both sides of the inequality by 2 to make the coefficient of variable-n equal to 1.
$\Rightarrow n>\dfrac{32}{2}$
$\Rightarrow n>16$
Here, we have obtained our inequality in the simplest form and variable-n is greater than 16. Therefore, the solution of the inequality $2n-7>25$ is $n\in \left( 16,\infty \right)$.

Note: We have put 16 in parentheses because 16 is not included in the solution set interval of the equation. If we had to include 16 in the solution set interval of the solution, then we would have used the square brackets instead of parentheses. Generally, in mathematics, two kinds of brackets are used to write various interval values. The parentheses which are symbolized as (), are used to represent that the values enclosed within the solution set interval whereas the square brackets which are symbolized as [], are used to represent that the numerical values enclosed within them are not included in the solution set.