Writing and Graphing Inequalities
Aligned to 6.EE.B.8 — Common Core State Standards for Mathematics.
What this lesson teaches
An inequality like x > c or x < c describes a whole range of numbers, not just one. On a number line, use an open circle at c (c is not included) and shade the direction that makes it true.
Worked examples
Example 1
'You must be older than 12 to ride' becomes a > 12. Graph it with an open circle at 12 and an arrow shading to the right, covering 13, 14, and beyond.
Example 2
'The elevator holds at most 8 people' becomes p ≤ 8. Graph it with a closed circle at 8 and shading to the left, because 8 itself is allowed.
Example 3
Open circle means 'not included' (> or <); closed circle means 'included' (≥ or ≤). That dot is the whole difference between 'more than 12' and '12 or more'.
Practice questions
- Write an inequality for 'a number x is less than 9'.
- Graph the solution to x > 4 on a number line.
- A ride requires a height of at least 48 inches. Write and describe the inequality for allowed heights.
Watch the lesson
Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.
▶ Watch this lessonEn español
Escribir y Graficar Desigualdades
Una desigualdad como x > c o x < c describe todo un rango de números, no solo uno. En la recta numérica, usa un círculo abierto en c (c no se incluye) y sombrea la dirección que la hace verdadera.
Ejemplo 1: 'Debes tener más de 12 años para subir' se convierte en a > 12. Grafícalo con un círculo abierto en 12 y una flecha sombreada a la derecha, cubriendo 13, 14 y más.
Ejemplo 2: 'El elevador lleva a lo más 8 personas' se convierte en p ≤ 8. Grafícalo con un círculo cerrado en 8 y sombreado hacia la izquierda, porque el 8 sí se permite.
Ejemplo 3: El círculo abierto significa 'no incluido' (> o <); el cerrado significa 'incluido' (≥ o ≤). Ese punto es toda la diferencia entre 'más de 12' y '12 o más'.
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