mathman said:
Linear inequalities are mathematical expressions that compare two values using the symbols <, >, ≤, or ≥. They represent a range of possible values that satisfy the inequality statement.
A linear equation is an expression that sets two values equal to each other, while a linear inequality compares two values and shows the relationship between them. Inequalities can have multiple solutions, while equations only have one solution.
To graph a linear inequality, first solve for y to put the expression in slope-intercept form. Then, plot the y-intercept and use the slope to plot additional points. Finally, shade the area above or below the line, depending on the inequality symbol.
To solve a system of linear inequalities, graph each inequality separately and find the overlapping region. The overlapping region represents the solutions that satisfy all of the inequalities in the system. This can also be done algebraically by solving each inequality for y and then finding the common solution set.
The most common error made when working with linear inequalities is forgetting to reverse the inequality symbol when multiplying or dividing by a negative number. This is because multiplying or dividing by a negative number changes the direction of the inequality. It is important to always double check the direction of the inequality after performing any operations.