Sketching Inequalities and Finding the Region Satisfied By Inequalities

The only real way to solve multiple inequalities of the formetc is to put all the inequalities on the same diagram and find the region satisfying all the inequalities as a part of theplane.

Example: Find the region satisfying the three inequalities Label this region with the letter

The lineis drawn. We want the region below the line so we shaded the region we do not want – above the line.

The lineis drawn. We want the region above the line so we shade the region we do not want – below the line.

The lineis drawn. We want the region below the line so we shade the region we do not want – above the line.

All the lines are solid because points on the line may satisfy the inequalities.

The region we want is the triangle in the middle, labelled R.