How to Graph Solutions to Linear Inequalities?

Step 1: Identifying the inequality you want to graph

Step 2: Rewrite the inequality

Step 3: Draw a number line and label it

Step 4: Draw a circle on the number line

Step 5: Draw an arrow pointing in the direction

Step 6: Label the shaded region to indicate which inequality it represents

Step 7: Repeat these steps for any additional inequalities that you need to graph

Graphing Solutions to Linear Inequalities – Examples 1

Solution:

Graphing Solutions to Linear Inequalities – Examples 2

Solution:

To graph this inequality on a number line, we need to isolate the variable \(x\) on one side of the inequality. Adding \(6x\) to both sides, we get:

\(2x + 2 ≥ -1\)

Now, subtracting \(2\) from both sides, we get:

\(2x ≥ -3\)

Finally, dividing both sides by \(2\), we get:

\(x ≥ -\frac{3}{2}\)

To graph this solution on a number line, we start by drawing a line and marking a point at \(-\frac{3}{2}\). Since \(x\) is greater than or equal to \(-\frac{3}{2}\), we shade the region to the right of the point. The graph should look like this:

Exercises for Graphing Solutions to Linear Inequalities

Graph the solution of each inequality.

1. \(\color{blue}{4x+3\ge 2x+11}\)
2. \(\color{blue}{\frac{x}{9}-6\le 4}\)

• \(\color{blue}{4x+3\ge 2x+11}\)

• \(\color{blue}{\frac{x}{9}-6\le 4}\)