Mathematics
Grade 7
15 min
Graph inequalities on number lines (Tutorial)
Graph inequalities on number lines (Tutorial)
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Identify and differentiate between the four inequality symbols: <, >, ≤, ≥.
Determine whether to use an open or closed circle when graphing an inequality on a number line.
Correctly shade the portion of the number line that represents the solution set of an inequality.
Graph simple one-variable inequalities (e.g., x > 5, y ≤ -2) on a number line.
Interpret the meaning of a graphed inequality on a number line.
Translate real-world scenarios into inequalities and represent them graphically.
Ever wonder how stores decide 'Must be 18 or older to buy this' or how speed limits are set? 🚦 These are all about inequalities!
In this lesson, you'll learn how to visually represent inequalities on a number line. This skill helps us understand...
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Key Concepts & Vocabulary
TermDefinitionExample
InequalityA mathematical statement that compares two expressions using an inequality symbol (<, >, ≤, ≥).`x < 7` means 'x is less than 7'.
Number LineA straight line on which every point corresponds to a real number, ordered from least to greatest.A line with tick marks for -3, -2, -1, 0, 1, 2, 3.
Open Circle (Hollow Circle)Used on a number line to indicate that the endpoint is NOT included in the solution set. Used for `>` (greater than) or `<` (less than).For `x > 3`, an open circle is placed at 3.
Closed Circle (Solid Circle)Used on a number line to indicate that the endpoint IS included in the solution set. Used for `≥` (greater than or equal to) or `≤` (less than or equal to).For `x ≤ 5`, a closed circle is placed at 5.
VariableA symb...
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Core Formulas
Rule for Open Circles
If an inequality uses `>` or `<`, the endpoint on the number line is represented by an open circle.
This means the number at the circle's position is *not* part of the solution. For example, for `x < 5`, 5 itself is not included.
Rule for Closed Circles
If an inequality uses `\ge` or `\le`, the endpoint on the number line is represented by a closed circle.
This means the number at the circle's position *is* part of the solution. For example, for `x \ge -2`, -2 itself is included.
Rule for Shading Direction (Variable on Left)
When the variable is on the left side of the inequality (e.g., `x < a` or `x > a`):
- If the symbol is `>` or `\ge`, shade to the **right** of the circle.
- If the symbol is `<` or `\le`, shade t...
5 more steps in this tutorial
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Challenging
A student's graph for the phrase 'a number is at most 2' shows a closed circle at 2 and shading to the right. Which statement best describes the error(s)?
A.The circle should be open, and the shading is in the wrong direction.
B.The circle is correct, but the shading is in the wrong direction.
C.The shading is correct, but the circle should be open.
D.The circle should be at 0, and the shading is in the wrong direction.
Challenging
A movie theater offers a discount for people who are younger than 13 years old. If `a` represents age, which inequality and graph correctly represent the ages that get a discount?
A.a ≤ 13, with a closed circle at 13 and shading to the left.
B.a < 13, with an open circle at 13 and shading to the left.
C.a > 13, with an open circle at 13 and shading to the right.
D.a ≥ 13, with a closed circle at 13 and shading to the right.
Challenging
The numbers -1, 0, and 0.5 are all solutions to an inequality `x < b`, but 1 and 1.2 are not. Based on this information, what must be the boundary value `b`?
A.0.5
B.0
C.1
D.-1
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