Mathematics
Grade 8
15 min
Write inequalities from number lines
Write inequalities from number lines
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1
Introduction & Learning Objectives
Learning Objectives
Identify the boundary point and its meaning on a number line.
Differentiate between open and closed circles and select the correct corresponding inequality symbol.
Determine the direction of an inequality (less than or greater than) based on the shaded region of a number line.
Write a simple one-variable inequality (e.g., x > 5) from its graphical representation.
Write a compound inequality (e.g., -1 ≤ x < 4) from its graphical representation.
Accurately use the symbols <, >, ≤, and ≥ to model a solution set shown on a number line.
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Key Concepts & Vocabulary
TermDefinitionExample
InequalityA mathematical statement that compares two values that are not necessarily equal. It uses symbols like < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to).The statement `p < 10` is an inequality meaning 'p is less than 10'.
Boundary PointThe specific number on a number line where an inequality starts or ends. It is marked with either an open or a closed circle.For a graph representing all numbers greater than 3, the number 3 is the boundary point.
Open CircleA hollow circle on a boundary point (e.g., ⚪) that indicates the number is NOT included in the solution set. It is used for 'less than' (<) and 'greater than' (>) inequalities.A number line for `x > -1` would have...
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Core Formulas
Circle Type Rule
Open Circle ⟹ < or >; Closed Circle ⟹ ≤ or ≥
The type of circle on the boundary point tells you whether to include 'or equal to'. An open (hollow) circle means the point is excluded (<, >). A closed (solid) circle means the point is included (≤, ≥).
Shading Direction Rule
Shading to the Right ⟹ > or ≥; Shading to the Left ⟹ < or ≤
The direction of the shading indicates whether the solution set contains numbers that are greater than or less than the boundary point. The inequality symbol should 'point' in the same direction as the shading.
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Challenging
A number line graph represents the inequality -3.5 ≤ x < 2. Which of the following numbers is NOT in the solution set?
A.-3.5
B.0
C.2
D.-1
Challenging
The sign at a water park ride says, 'Riders must be at least 48 inches tall.' If 'h' represents a rider's height, which number line correctly graphs the acceptable heights?
A.closed circle on 48 with shading to the right.
B.An open circle on 48 with shading to the right.
C.closed circle on 48 with shading to the left.
D.An open circle on 48 with shading to the left.
Challenging
A number line shows a closed circle on -1, an open circle on 4, and shading between them. A student incorrectly writes the inequality as 4 > x ≥ -1. Which common pitfall does this specific error represent?
A.Confusing open and closed circles.
B.Reversing the inequality symbol direction.
C.Using the wrong boundary points.
D.Incorrectly ordering a compound inequality.
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