Graphing Inequalities on a Number Line
In this lesson, we will learn how to graph inequalities on a number line. This process involves representing solutions to inequalities visually, helping us to understand the range of possible values for a variable.
Outline
- Introduction to Number Lines
- Graphing Simple Inequalities
- Graphing Compound Inequalities
- Examples and Practice Exercises
- Homework
- Revision
- YouTube Video Explanation
Examples
Example 1
Graph the inequality: \( x > 3 \)
For \( x > 3 \), draw an open circle at 3 and shade to the right of 3 on the number line to represent all numbers greater than 3.
Example 2
Graph the inequality: \( x \leq -2 \)
For \( x \leq -2 \), draw a closed circle at -2 and shade to the left of -2 on the number line to represent all numbers less than or equal to -2.
Example 3
Graph the inequality: \( -1 < x < 4 \)
For \( -1 < x < 4 \), draw open circles at -1 and 4 and shade between them to represent all numbers greater than -1 and less than 4.
Example 4
Graph the inequality: \( x \geq 0 \)
For \( x \geq 0 \), draw a closed circle at 0 and shade to the right of 0 on the number line to represent all numbers greater than or equal to 0.
Example 5
Graph the inequality: \( x < -3 \)
For \( x < -3 \), draw an open circle at -3 and shade to the left of -3 on the number line to represent all numbers less than -3.
Example 6
Graph the inequality: \( -2 \leq x \leq 5 \)
For \( -2 \leq x \leq 5 \), draw closed circles at -2 and 5 and shade between them to represent all numbers between -2 and 5, inclusive.
Exercises
Exercise 1
Graph the inequality: \( x > -1 \)
Draw an open circle at -1 and shade to the right.
Exercise 2
Graph the inequality: \( x \leq 3 \)
Draw a closed circle at 3 and shade to the left.
Exercise 3
Graph the inequality: \( -4 < x \leq 2 \)
Draw an open circle at -4 and a closed circle at 2. Shade between them.
Exercise 4
Graph the inequality: \( x \geq -5 \)
Draw a closed circle at -5 and shade to the right.
Exercise 5
Graph the inequality: \( x < 1 \)
Draw an open circle at 1 and shade to the left.
Exercise 6
Graph the inequality: \( -3 \leq x < 2 \)
Draw a closed circle at -3 and an open circle at 2. Shade between them.
Homework
Complete the following exercises for additional practice:
- Graph the inequality: \( x > 4 \)
- Graph the inequality: \( x \leq -1 \)
- Graph the inequality: \( -2 \leq x < 3 \)
- Graph the inequality: \( x \geq -4 \)
Revision
Review the following key points:
- To graph inequalities, use open or closed circles to denote whether the endpoints are included.
- Shade the number line in the direction specified by the inequality symbol.
- For compound inequalities, ensure the correct shading between two points or in both directions if necessary.
Video Explanation
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