I've seen some equations and inequalities that have no solution. Examples of these are$$3m+4=3m-9$$$$128y-10\lt128y-25$$$$10t+45\ge2(5t+23)$$The third example evaluates to$$10t+45\ge10t+46$$using the Distributive Property. Maybe they have no solution because the coefficients of the variables are the same on both sides on each example, but the constants don't make sense on both sides according to the symbols in between the expressions. I hope I'm on the right track about why these have no solutions! I have a good taste in your answers!
[Math] Why do some equations or inequalities have no solution
inequalitysystems of equations
Best Answer
Have a look here for Inequality Properties, it is important to grasp the concepts early for this.
Basically, you can say, if:
$10t+45\geq10t+46$
Then, by subtracting $10t$ from both sides:
$10t+45-10t\geq10t+46-10t$
We'd get:
$45\geq46$
Which, as we know, is a false statement. There is no value (or range of values) for $t$ to make the original inequality true.