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)`.