How to Graph and Solve Inequalities with Interval Notation

TL;DR

To graph and solve inequalities, first determine if the circle is open or closed based on the inequality sign, then shade in the appropriate direction on the number line. Solutions are represented in interval notation, which showcases the range of values satisfying the inequality, including cases with fractions and variables on both sides.

Transcript

in this video we're going to focus on graphing inequalities on number lines and also solving inequalities we're going to solve inequalities with fractions variables on both sides absolute value and we're also going to write the answer in interval notation so let's begin let's say if x is greater than 2 how can you represent this inequality on a num... Read More

Key Insights

• 😚 Graphing inequalities on number lines involves determining open or closed circles and shading in the appropriate direction based on the inequality sign.
• 🧡 The interval notation is used to represent the solutions of inequalities, indicating the range of values that satisfy the inequality.
• 😑 Absolute value inequalities can be solved by writing two equations with the positive and negative versions of the absolute value expression and finding the common solution.
• 🙃 Inequalities with fractions and variables on both sides can be solved using inverse operations to isolate the variable.

Questions & Answers

Q: How do you graph the inequality x > 2 on a number line?

To graph x > 2, you need an open circle at 2 and shade to the right, representing all values greater than 2. The interval notation for this is (2, ∞).

Q: What is the solution and interval notation for x ≥ -1?

To graph x ≥ -1, you need a closed circle at -1 and shade to the right. The interval notation for this is [-1, ∞].

Q: How do you represent the inequality x < 4 on a number line?

To graph x < 4, you need an open circle at 4 and shade to the left, representing all values less than 4. The interval notation for this is (-∞, 4).

Q: What is the solution and interval notation for x ≤ -2?

To graph x ≤ -2, you need a closed circle at -2 and shade to the left. The interval notation for this is (-∞, -2].

Q: How do you graph the inequality x > 1 and x ≤ 4 on a number line?

For x > 1, you need an open circle at 1 and shade to the right. For x ≤ 4, you need a closed circle at 4 and shade to the left. The intersection of the shaded regions represents the common solution. The interval notation for this is (1, 4].

Q: How do you graph the inequality x < -2 or x ≥ 3 on a number line?

For x < -2, you need an open circle at -2 and shade to the left. For x ≥ 3, you need a closed circle at 3 and shade to the right. The union of the shaded regions represents the solution. The interval notation for this is (-∞, -2] ∪ [3, ∞).

Summary & Key Takeaways

• The video explains how to graph inequalities on number lines and solve them, covering topics such as open and closed circles, shading, and interval notation.

• It provides examples of graphing and solving inequalities, including cases with fractions and variables on both sides of the inequality.

• The solutions are represented in interval notation, which shows the range of values that satisfy the inequality.