Example 221

Sketch in the xy-plane the set of all pairs of numbers (x. y) that satisfy the inequality 2x + y < 4. (Using set notation, this is {(x. y) :2x + y < 4}.)

Solution The inequality can be written as y < —lx+4. The set of points (x, >•) that satisfy the equation y = —2x + 4 is a straight line. Therefore, the set of points (x, y) that satisfy the inequality >• < —2x +4 must have y-values below those of points on the line y = —2x + 4. So it must consist of all points that lie on or below this straight line. See Fig. 2.40.

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