Systems of inequalities with one unknown. Numerical intervals
Several inequalities with one unknown considered together form a system of inequalities. A solution of the system is a value of the unknown that makes all the inequalities true at once. So we solve each inequality separately and then find the common part of the solutions on the number line. The set of numbers with a < x < b is the interval (a; b), and a ≤ x ≤ b is the segment [a; b]; a ≤ x < b and a < x ≤ b are half-intervals written [a; b) and (a; b]. The sets x > a, x ≥ a, x < a, x ≤ a are rays: (a; +∞), [a; +∞), (-∞; a), (-∞; a]. A square bracket includes the endpoint, a round bracket does not. If there is no common part, the system has no solution.
“Shading on the number line”: two pupils each shade the solution of one inequality in a different colour; the doubly shaded part is the solution of the system.