Mathematics
Grade 8
15 min
Graph inequalities on number lines
Graph inequalities on number lines
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Identify the four basic inequality symbols and their meanings.
Distinguish between open and closed circles when graphing inequalities.
Determine the correct direction to shade on a number line based on an inequality.
Graph simple one-variable inequalities on a number line.
Interpret a given graph of an inequality on a number line.
Represent real-world scenarios using inequalities and graph them.
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In this lesson, you'll learn how to visually represent inequalities on a number line. This skill helps us understand ranges of numbers that satisfy certain conditions, which is super useful in math and everyday life.
Real-World Applications
Minimum height requir...
2
Key Concepts & Vocabulary
TermDefinitionExample
InequalityA mathematical statement that compares two expressions using an inequality symbol (e.g., <, >, ≤, ≥).x > 5 means 'x is greater than 5'.
Number LineA line on which numbers are marked at regular intervals, used to represent real numbers visually.A line with 0 in the middle, positive numbers to the right, and negative numbers to the left.
Open CircleA hollow circle (⚪) used on a number line to indicate that a specific number is *not* included in the solution set of an inequality.Used for > (greater than) or < (less than) inequalities.
Closed CircleA filled-in circle (⚫) used on a number line to indicate that a specific number *is* included in the solution set of an inequality.Used for ≥ (greater than or equal to) or ≤ (less than or e...
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Core Formulas
Circle Type Rule
If the inequality symbol is > or <, use an open circle (⚪) at the critical value. If the symbol is ≥ or ≤, use a closed circle (⚫) at the critical value.
This rule tells you whether the boundary number itself is part of the solution set.
Shading Direction Rule
If the inequality is written with the variable on the left (e.g., x > a or x < a), the arrow of the inequality symbol points in the same direction as the shading on the number line. Specifically, for x > a or x ≥ a, shade to the right. For x < a or x ≤ a, shade to the left.
This rule helps you quickly determine which side of the critical value contains the solutions.
Variable Position Rule
Always ensure the variable is on the left side of the inequality before applying the sha...
5 more steps in this tutorial
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Challenging
The inequality `k ≥ -1` is graphed. Then, the inequality is changed to `k < -1`. How does the graph change?
A.The circle becomes open, and the shading direction stays the same.
B.The circle becomes open, and the shading direction reverses.
C.The circle stays closed, and the shading direction reverses.
D.The circle becomes closed, and the shading direction reverses.
Challenging
A student graphed the inequality `7 > x`. Their graph has an open circle at 7 and shading to the right. Which statement correctly identifies their error(s)?
A.They did not rewrite the inequality as x < 7, which caused them to shade in the wrong direction.
B.They used an open circle instead of a closed circle.
C.They used an open circle and shaded in the wrong direction.
D.They should have put the circle at 0 instead of 7.
Challenging
The graph of an inequality shows a closed circle at a number 'c' and shading to the left. The number -5 is in the solution set, but the number -3 is not. Which of the following could be the inequality?
A.x ≤ -3
B.x ≤ -5
C.x ≤ -6
D.x ≤ -4
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