Question

Please help me with problem 2 of Inequalities in Two Variables

Answer 1

With inequalities,

< means less than

> means greater than.

Both are represented by a dotted line.

&le; means less than or equal

&ge; means greater than or equal,

Both are represented by a solid line.

To construct the inequality x<2 we would switch the < to an equal sign, and construct the equality, namely x=2, which is a vertical line passing through (2,0).

From the previous comments, we know that x<2 is a dotted line.

Now we have to decide the inequality applies to which side of the line.

One way is to take some test points, e.g. the origin (0,0) where x=0.

Since x=0 is less than two, we know that (0,0) satisfies the inequality, so the area to the left of the vertical line (x=2) satisfies the inequality.

Hence the proper graph would show the left side shaded, but at x=2, the vertical line should be dotted.

An even simpler rule to find the region is to see that "x < something" is to the left, and "x > something" is to the right of a vertical or a slanted line.