Solving Inequalities Chapter 2.7

Linear Inequalities Graph the indicated line – Solid line { } – Dotted line { } Choose a point not on the line to test – If point satisfies inequality, shade region containing that point – If point does not satisfy inequality, shade the other region

Example Linear Inequality y > 2x +1 – y-intercept at (0, 1) – slope is 2 Up 2, over 1 Sketch solid line Test point – (0, 0) – y > 2x -1 – 0 > 2(0) – 1 – 0 > -1 true – Shade this side

Example Linear Inequality y < -3/2x +2 – y-intercept at (0, 2) – slope is -3/2 Down 3, over 2 Sketch dotted line Test point – (0, 0) – y < -3/2x +2 – 0 < -3/2(0) +2 – 0 < 2 true – Shade this side

Example Linear Inequality y < -2x – y-intercept at (0, 0) – slope is -2 Down 2, over 1 Sketch dotted line Test point – (0, 1) – y < -2x – 1 < -2(0) – 1 < 0 not true – Shade other side

Absolute Value Inequalities Decide where to put the vertex of your graph – Positive number inside: move left|x+2| – Negative number inside: move right|x-3| – Positive number outside: move up|x|+1 – Negative number outside: move down|x|-2 Sketch your v-shape Test a point that is not on the graph – If point satisfies inequality, shade region containing that point – If point does not satisfy inequality, shade the other region

Example Absolute Value Inequality y > |x| +1 – Vertex does not move left or right – Vertex moves 1 unit up – Plot points 1 unit up in both directions to make ensure a nice shape Sketch dotted v-shape Test (0, 0) – y>| x | +1 – 0>| 0 |+1 – 0>1 not true – Shade other side

Example Absolute Value Inequality y < |x-1| -2 – Vertex moves 1 unit right – Vertex moves 2 units down – Plot points 1 unit up in both directions Sketch solid v-shape Test (0, 0) – y < |x - 1| - 2 – 0 < | 0 - 1| - 2 – 0 < |-1| - 2 – 0 < – 0 < -1 not true – Shade other side

Assignment Graphing Inequalities worksheet – Work on your own quietly – I’ll be around to help Finish for homework