# Lesson 21

From One- to Two-Variable Inequalities

• Let’s look at inequalities in two dimensions.

### 21.1: Describing Regions of the Plane

For each graph, what do all the ordered pairs in the shaded region have in common?

### 21.2: More or Less

1. Write at least 3 values for $$x$$ that make the inequality true.
1. $$x < \text{-}2$$
2. $$x+2 > 4$$
3. $$2x-1 \leq 7$$
2. Graph the solution to each inequality on a number line.

3. Using the inequality $$x < \text{-}2$$, write 3 coordinate pairs for which the $$x$$-coordinate makes the inequality true. Use the coordinate plane to plot your 3 points.

### 21.3: Above or Below the Line

1. Graph the line that represents the equation $$y = 3x-4$$

2. Is the point $$(4,8)$$ on the line?
1. Explain how you know using the graph.
2. Explain how you know using the equation.
3. Use the 3 points $$(5, a), (\text-7,b)$$ and $$(c,20)$$
1. Write values for $$a, b,$$ and $$c$$ so that the points are on the line.
2. Write values for $$a, b,$$ and $$c$$ so that the points are above the line.
3. Write values for $$a, b,$$ and $$c$$ so that the points are below the line.