The interval method
Mark the roots on the number line, put a sign on each gap and read the solution of an inequality such as (x + 1)x − 4x − 2 ≤ 0.
- Russia: grade 9
Guide
Break the expression into factors x − a. Mark the roots on the line: they cut it into gaps. On a gap the expression keeps its sign, and it can change only at a root.
Right of the largest root the sign is + when every factor has a positive coefficient of x. At a root of odd multiplicity the sign flips; at a root of even multiplicity it stays.
With ≤ or ≥ the roots of the top are filled dots. The roots of the bottom are always hollow: you cannot divide by 0.
The factor rows are given; you fill in the result row. Tap a cell to change +, − or blank. Then draw the answer on the line.