Question

How do you solve 2r – 5 > 2r – 5?

Answer 1

Hint: In this particular problem, the given equation has to be solved which is in the form of a linear equation in one variable. Also know that the general form of the equation of a straight line is y = mx + c which is to be used. Hence, the equation has to be converted in the form of y = mx + c. The obtained value will be finally plotted on the graph.

Complete step-by-step answer:
Now, let’s discuss the question now.
We already know that the slope-intercept form is a general form of a straight line and can be expressed as y = mx + c where ‘m’ is a slope and c is a constant and intercepts are m and c. So, if we wish to plot a straight line, first we have to convert the given equation in a slope-intercept form.
Now, write the equation given in question.
$\Rightarrow $2r – 5 > 2r – 5
Take the like terms on one side and constants on the other side of the equation.
$\Rightarrow $2r – 2r > 5 – 5
On solving further we will obtain zero on both sides. So, there is no solution for this equation.

Note: There is another way of solving this question. As we can see that both sides of the inequality are the same expression and both sides of the inequality are always equal. And the inequality operator is a greater than operator and does not contain an “or equal to” clause also. Therefore, this inequality is never true and the solution is the null or empty set:
R = $\left\{ \phi \right\}$