Systems of Inequalities with one Variable

We say that several inequalities form a system, if we need to find common solutions of given inequalities.

Value of variable for which every inequality in the system becomes correct is called a solution of the system of inequalities.

Example. Solve system of inequalities `{(5x+2>3x-1),(3x+1>7x-4):}`.

Let's transform first inequality into equivalent inequality:

`5x+2>3x-1`;

`5x-3x> -1-2`;

`2x> -3`;

`x> -3/2=-1.5`.

Now let's transform second inequality into equivalent inequality:

`3x+1>7x-4`;

`3x-7x> -4-1`;

`-4x> -5`;

`x< 5/4=1.25`.

Therefore, equivalent system is `{(x> -1.5),(x<1.25):}`.

Using coordinate line, we found that required set of solutions is `(-1.5;1.25)`.