Linear Inequalities and Systems of Linear Inequalities Objective: Students will be able to graph and identify linear inequalities in real world situations.

Linear Inequalities Very Similar to linear equations Solve inequality for y Graph line like normal If just greater than or less than you use a dashed lines, similar to an open circle If it is also equal to you use a solid line Then you have to shade the graph because there are multiple solutions To do this test a point not on the line If the equation come back true shade on that side of the line If it comes back false shade on the other side of the line

Examples

Example Solve for y and graph

Systems of Linear Inequalities Similar to other systems we did You have multiple lines to graph and shade You are looking for the overlapping region of feasible region of all the lines Don’t shade heavy to begin with just draw arrows to indicate direction and when all lines are drawn and arrows indicated shade the main overlapping region

Example

Writing Linear Inequalities Again similar to writing equations of lines from a graph Determine slope Find y –intercept Is line solid or dashed indicates inequality Pic a point in the shaded region, sub into equation to help determine which inequality to use

Examples

Word Problems Be able to write the inequality from a word problem and then graph it to get solutions