Question

How do I graph an inequality in one variable? Hint: Think number line.

A) By plotting points on a Cartesian plane
B) By using a bar graph
C) By representing it on a number line
D) By creating a pie chart

Answer 1

To graph an inequality in one variable, represent it on a number line by plotting the critical points and shading the appropriate region. Identifying the type of inequality and using open and closed circles are important steps in the process. The correct answer is option B .

Step-by-step explanation:

To graph an inequality in one variable, you can represent it on a number line. A number line is a line that represents all real numbers, with positive numbers to the right of zero and negative numbers to the left. Here are the steps to graph an inequality on a number line:

1. Identify the inequality and determine if it is a greater than (>), less than (<), greater than or equal to (≥), or less than or equal to (≤) inequality.
2. Plot the critical points on the number line. The critical points are the values that satisfy the inequality. For example, if the inequality is x > 2, you would plot a point at 2 and make an open circle to represent that 2 is not included in the solution set.
3. Draw an arrow to the right of the critical point if the inequality is greater than (>), or to the left if the inequality is less than (<). If the inequality is greater than or equal to (≥) or less than or equal to (≤), use a closed circle to represent that the critical point is included in the solution set.
4. Shade the region on the number line that satisfies the inequality. If the inequality is greater than (>), shade the region to the right of the arrow. If the inequality is less than (<), shade the region to the left of the arrow. If the inequality is greater than or equal to (≥), shade the region including and to the right of the closed circle. If the inequality is less than or equal to (≤), shade the region including and to the left of the closed circle.