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:
Now let's transform second inequality into equivalent inequality:
`x/4+1>(3x)/2`; multiply both sides by 4:
Therefore, equivalent set is `x<4;x<0.8`.
Using coordinate line, we found that required set of solutions is `(-oo,4)`.