Locate and write down the inequality equation in question. As an example, use the equation.
3x + 6y > 14
Solve the linear equation for y in terms of x or , if the equation is already expressed in this form, skip this step and move to step 3. Pay attention to the order of operations as to how to manipulate and combine terms. The acronym PEMDAS represents the order of operation, which stands for parentheses, exponents, multiplication and division, and then addition and subtraction. Continuing with the example 3x + 6y > 14:
Start by subtracting 3x from both sides:
3x + 6y - 3x > 14 - 3x
6y > 14-3x
Divide through by 6 to get y by itself
6y/6 > (14- 3x)/6
y > (14-3x)/6
Convert the inequality sign into an equal sign. Continuing with our example, this is
y = (14 - 3x)/6
Plot the linear equation from step 3. Continuing with the example equation, draw an x-y graph labeling both the x and y axis from 1 to 10. Start with x = 1. At x = 1, y is 11/6 or 1.83. Plot the point (1, 1.83) on the graph. At x = 2, y is 8/6 or 1.33. Plot the point (2, 1.33) on the graph. At x = 3, y is 5/6 or 0.83. Plot the point (3, 0.83). With three points, you can draw the graph. Take a ruler and trace a line through the three points.
Present the inequality on the graph by shading in the appropriate area. Continuing with the example, given that the inequality for this example is a greater than sign, it represents the area of the graph where the values of y is greater than the line. Therefore, you will shade in the area where the values of y is above the line.