# 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).