Linear Inequalities Notes

University:
Eastern Kentucky University
Course:
MAT 122 | Precalculus Mathematics
Academic year:

2022
Views:

85

Pages:

1
Author:

Trevon Bernard

Page # 1 LINEAR INEQUALITIES LINEAR INEQUALITIES 1. Linear inequations in one variable are x  a, x 4. To find the graphical solution of system of  a, x > a, x < a, y  a, y  a, y < a, y > inequations in one variable we proceed as point a. System of inequation in one variable is the 2 and point 3 and the common shaded portion combination of inequations. represents the solution set. 2. To draw the graphical solution of x  a, x  a, x > a , x < a: we keep the following points in consideration. (i) First we draw graph of x = a which is a line. For this equation x is always a and x can take any value 5. Linear inequations in two variables are (i) ax + by + c  0 (ii) ax+by + c  0 (iii) ax + by + c > 0 (iv) ax+by +c < 0. Their combination is known as a system of linear inequations in two variables. 6. To find the graphical solution of linear inequation in two variables we follow as under : x a a a y 0 1 2 etc. (i) Consider the equation ax + by + c =0 and find the values of x and y which satisfy the and its graph is a line parallel to y-axis. (ii) We draw a line if x  a, x  a and a dotted line if x > a, x < a. equation. Find at least three such ordered pairs (x, y) and plot these on a graph. Graph is a straight line. We draw a line for in equation ax + by + c  0 or ax + by + c  0 and a dotted (iii) Take any point in the plane, not on the line line for the inequation ax + by + c > 0 or ax and put in inequation x  a, x  a, x > a or x + by + c < 0. < a. If it is a true statement then we shade the portion containing the point as the solution set and if it is a false statement we shade the portion not containgin the point as solution set. 3. To draw the graphical solution of y  a, y  a, y > a or y < a : (ii) Take any point in a plane not lying on the line (generally we take (0, 0) if it does not lie on a point) and put in the given inequation. If it is a true statement we shade the portion containing that point and if it is a false statement we shade the portion not containing (i) We consider the equation y = a and draw its graph. For the equation y = a, is always a, can take any value. the point under consideration. 7. To find the graphical solution of system of linear inequations, we draw the graphical solution of inequations in the system and the common x 0 1 2 y a a a shaded portion represents the solution of system etc. of inequations. 8. |x–a|  b  x  a + b or x  a – b. Its graph is a line parallel to x-axis and the follow parts (ii), (iii) of point 2 9. |x–a|  b  a – b  x  a + b.