What is the sign scheme method Can you explain it briefly - Maths - Linear Inequalities

Question

What is the sign scheme method Can you explain it briefly?

Gursheen kaur. · Accepted Answer

Sign scheme method : It helps us to determine the interval of an inequality Therefore, there are two sign scheme methods 1) Quadratic inequality 2) Rational integrity inequality Now, lets take an example: $x^{2} - 4 \leq 0 (x + 2) (x - 2) \leq 0 t h e r e f o r e, - 2 \leq x \leq 2$ thus, the interval of inequality lies b/w -2 and 2 as follows:

Example 2) $| x + 1 | > 3 t h e r e f o r e, e i t h e r x + 1 < - 3 o r x + 1 > 3 x < - 4 o r x > 2 [∵ | x | > l, e i t h e r x < - l o r x > l]$ thus, the solution set consists of all real nos which are less than -4 or all real nos which are greater than 2 it can be represented as follows:

example 3) $x^{2} - 5 x + 6 \geq 0 x^{2} - 2 x - 3 x + 6 \geq 0 x (x - 2) - 3 (x - 2) = 0 (x - 3) (x - 2) \geq 0 e i t h e r x - 3 \geq 0 o r x - 2 \geq 0 3 \leq x < \infty o r - \infty < x \leq 2 t h u s, t h e int e r v a l i s (- \infty, 2] \cup [3, \infty)$ it can be represented as follows:

What is the sign scheme method.Can you explain it briefly?