matching graphs inequailty

Huh?

To solve an inequality involving graphs, you need to follow these steps:

Step 1: Determine the type of inequality: Is it a greater than (>), less than (<), greater than or equal to (≥), or less than or equal to (≤) inequality?

Step 2: Graph each side of the inequality as if it were an equation. If it is a less than or greater than inequality, use a dashed line. If it is a less than or equal to or greater than or equal to inequality, use a solid line.

Step 3: Shade the area that satisfies the inequality. To do this, select a test point not on the line you graphed and substitute its coordinates into the inequality to determine if it is a true or false statement. If it is true, shade that region on the graph. If it is false, shade the other region.

Step 4: Write the answer in interval notation or as a set of inequalities, depending on the format requested.

Let's take an example to illustrate this process:

Example:
Solve the inequality 3x - 4 > 2x + 1.

Step 1: Determine the type of inequality:
Since the inequality sign is greater than (>), it is a greater than inequality.

Step 2: Graph each side of the inequality:
Graph the line y = 3x - 4 with a dashed line since it is a greater than inequality.

Step 3: Shade the appropriate region:
Select a test point that is not on the line, for example, (0,0). Substitute its coordinates into the inequality: 3(0) - 4 > 2(0) + 1. This simplifies to -4 > 1, which is false. Therefore, shade the region below the dashed line.

Step 4: Write the answer:
The solution set for this inequality is x < 5/3.
In interval notation, this can be written as (-∞, 5/3).