⁦Systems of linear inequalities in one variable⁩

⁦In Ukrainian Grade 9 algebra⁩ (§⁦6) systems of inequalities arise when several conditions must hold at once⁩. ⁦For example the expression √(٢x − ١) + √(٥ − x) makes sense only when ٢x − ١ ≥ ٠ and ٥ − x ≥ ٠ together⁩.

⁦A solution of a system of inequalities is a value of the variable that makes every inequality of the system true⁩. ⁦To solve the system means to find all its solutions or to show there are none⁩.

⁦Solve each inequality on its own, then look for the common part of the solutions⁩. ⁦On the number line it is the part covered by every arc⁩.

⁦A system can have a whole interval of solutions, just one number, or none⁩. ⁦Then the solution set is called empty⁩.

⁦The grey bands over the line show the solutions of the single inequalities⁩. ⁦Draw their common part on the line⁩.