Sign tables and fractional inequalities
Find where an expression is positive and where it is negative: mark the zeros, fill in a sign table under the number line, and read off the solution of an inequality such as x β 1x + 2 β₯ 0.
π Start here: read the steps of the βLessonβ in order (1, 2, 3 β¦) and answer each question. Then continue with βPracticeβ.
- France: grade 10
- Iran: grade 10
- Afghanistan: grade 9
- Syria: grade 10
- Palestine: grade 10
- Ukraine: grade 9
- Russia: grade 9
Guide
Extension: in the UK this is A-level work. Afghan students meet it in grade 9 and Iranian students in grade 10.
A binomial such as 2x β 4 is 0 at one point, x = 2. To the right of that point it has the same sign as the number in front of x; to the left, the opposite sign.
For a product or a quotient, give each factor its own row of signs. Dashed lines mark the zeros. In each gap, the result's sign follows the rule of signs: an even number of β makes +, an odd number makes β.
A zero of the top is a filled dot: there the expression is 0. A zero of the bottom is a hollow dot: there the expression has no value, so it is never in the answer.
Tap a cell to switch it between +, β and empty (or type + or β). Then tap the line to draw the answer: choose the shape with the buttons, and tap a dot to make it filled or hollow.