Question

How do you solve $2x-5 > 6$?

Answer 1

Hint: Now we want to find the given solution of the given equation. To solve the equation we will first separate the variables and constants. Now we will simplify the equation and hence we will find the value of x by dividing the equation with coefficient of x. Hence we get the required solution of the given equation. Now we will write the solution as an interval.

Complete step by step solution:
Now consider the given equation $2x-5>6$ .
Now we know that the given equation is an inequality in x.
Now to find the solution of the equation we will simplify the equation in the same way we simplify linear equations.
Now the first step is to separate the variables and the constants. To do so we will just transpose the term 5 from LHS to RHS. Hence we get the equation as,
$\begin{align}
  & \Rightarrow 2x>6+5 \\
 & \Rightarrow 2x>11 \\
\end{align}$
Now we want to find the values of x for which the equation is true. Hence to get x in the inequality we must divide the whole equation by 2.
$\Rightarrow x>\dfrac{11}{2}$
Hence the solution of the given equation is $x>\dfrac{11}{2}$
Hence the solution of the equation is $\left( \dfrac{11}{2},\infty \right)$

Note: Now note that while solving inequalities we solve and simplify in the same way we simplify linear equations. But in inequalities when we multiply the equation by a certain term the inequality remains the same if the term is positive and changes if the term is negative. Similarly if we divide the equation with positive term then the inequality remains the same but If we divide the inequality by negative term the inequality changes.