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Linear Inequalities in Two Variables

I. A First Example (p.313): Exercise #14

II. Basic Ideas:

a. Solution of an inequality is a “region” of
points whose (x,y) coordinates satisfy the
inequality.

b. The “boundary” line is defined by the
equation where the inequality is replaced with
an “=” sign.

c. Determination of the region containing the
solutions is found by “testing” a point not on
the boundary.

d. If a test point’s coordinates satisfy the
inequality then every point in the region will
also, but if they do not then none of the points
in that region will either.

e. The entire set of solutions is indicated by
shading the appropriate region.

III. More Examples (pp.312-313): Exercise #8,12

IV. Boundary Line Convention:

a. For either < or >, the boundary line is a
dashed line indicating its points are not
part of the solution set.

b. For either ≤ or ≥, the boundary line is a
solid line indicating its points are part of
the solution set.

V. A Last Example (p.313): Exercise #22

HW: pp.312-313 / Exercises # 1-17 (odd),21,23