In Exercises 1–26, graph each inequality. x≤−3

Verified step by step guidance

1. Identify the inequality: $x\le -3$. This means that $x$ can be any value less than or equal to $-3$.
2. Draw a number line to represent the possible values of $x$.
3. Locate the point $-3$ on the number line.
4. Since the inequality is $\le$, use a closed circle at $-3$ to indicate that $-3$ is included in the solution set.
5. Shade the region to the left of $-3$ on the number line to represent all values less than $-3$.

Key Concepts

Inequalities

Inequalities are mathematical expressions that show the relationship between two values when they are not equal. They use symbols such as ≤ (less than or equal to), ≥ (greater than or equal to), < (less than), and > (greater than). Understanding how to interpret and manipulate inequalities is essential for solving problems that involve ranges of values.

Graphing Linear Inequalities

Graphing linear inequalities involves representing the solutions of the inequality on a coordinate plane. For example, the inequality x ≤ -3 indicates that all values of x that are less than or equal to -3 should be shaded on the graph. The boundary line (in this case, x = -3) is solid, indicating that points on the line are included in the solution set.

Coordinate Plane

The coordinate plane is a two-dimensional surface defined by a horizontal axis (x-axis) and a vertical axis (y-axis). Each point on the plane is represented by an ordered pair (x, y). Understanding the layout of the coordinate plane is crucial for accurately graphing inequalities and visualizing their solutions.