# Set of Inequalities with One Variable

With say that several inequalities form a set, if we need to find solutions that satisfy at least one inequality.

Value of variable for which at least one inequality in the set becomes correct is called a solution of the set of inequalities.

Example. Solve set of inequalities (2x-3)/5>(3x-10)/2;\ x/4+1>(3x)/2.

Let's transform first inequality into equivalent inequality:

(2x-3)/5>(3x-10)/2; multiply both sides by 10:

4x-6> 15x-50;

11x< 44;

x<4.

Now let's transform second inequality into equivalent inequality:

x/4+1>(3x)/2; multiply both sides by 4:

x+4> 6x;

5x<4;

x< 4/5=0.8.

Therefore, equivalent set is x<4;x<0.8.

Using coordinate line, we found that required set of solutions is (-oo,4).