For the following linear inequalities draw the feasibile region
i: x _>1
ii: x+y _<2
iii: x-axis
2x-9=13
To draw the feasible region for each linear inequality, you need to visualize the solution space on a graph.
i: x ≥ 1
To graph this linear inequality, draw a vertical line passing through x = 1 on the x-axis. Shade the region to the right of the line, including the line itself. This represents all the points where x is greater than or equal to 1.
ii: x + y < 2
To graph this linear inequality, first rewrite it in slope-intercept form (y = mx + b): y < -x + 2. Start by plotting the line y = -x + 2 on the graph. This line has a y-intercept of 2 and a slope of -1 (down 1 unit for every 1 unit to the right). Then shade the region below the line, excluding the line itself. This represents all the points where the sum of x and y is less than 2.
iii: x-axis
To graph the x-axis, simply draw a horizontal line extending infinitely in both directions. Shade the entire line to represent all the points on the x-axis.
Once you have graphed each inequality, find the overlapping region between all of them. This overlapping region represents the feasible region.