Systems of linear inequalities in one variable
Solve each inequality of a system, show the solutions on a line and find their common part: a segment, a single number or the empty set.
- Palestine: grade 11
- Ukraine: grade 9
- Russia: grade 8
Guide
In Ukrainian Grade 9 algebra (§6) systems of inequalities arise when several conditions must hold at once. For example the expression √(2x − 1) + √(5 − x) makes sense only when 2x − 1 ≥ 0 and 5 − x ≥ 0 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.