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`.set of equations

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