## Curve Sketching - Solving Graphical Inequalities

To solve the equationcould turn out to be quite a tricky problem. To solve exactly you may have to factorise the cubic equation

There is a simple to solve the inequality approximately. You can sketch the curve and find thosevalues for whichThis will be the solution set of the inequality. The points to be plotted are shown in the table below.

-3 | -2 | -1 | 0 | 1 | 2 | 3 | |

-27 | -8 | -1 | 0 | 1 | 8 | 27 | |

-9 | -4 | -1 | 0 | -1 | -4 | -9 | |

15 | 10 | 5 | 0 | -5 | -10 | -15 | |

-21 | -2 | 3 | 0 | -6 | -6 | 3 |

The curve is sketched below.

To solve the inequality we find the intersection of the curve with the lineand read off the – values for those points of intersection.

The lineintersects the curve at the points whereand

The curve is less than, or below the lineforand