Lesson 5: Understand Inequalities and Their Solutions6.AT.9

I can…

I can graph the solutions of an inequality on a number line.

Key words

• Graph Inequalities — Show all the answers on a line with a dot and arrow.
• Number line — A line with numbers in order, left to right.
• Open circle — An empty circle. The number is left out.
• Closed circle — A filled circle. The number is part of the answer.
• Solution set — All the values that make the sentence true.
• Inequality — A math sentence that compares sides with <, >, ≤, or ≥.
• Boundary point — The number at the edge of the solutions on a number line.
• True statement — A math sentence that is correct.

Steps

1. Graph t ≥ 2. The boundary number is 2.
2. The symbol ≥ includes 2, so I draw a closed (filled) circle at 2.
3. 'Greater than or equal to' means larger values work, so I shade to the right.
4. Now the graph shows 2, 3, 4, and every value above 2.

Try it

How would you graph the inequality x < 4?

Check your answer

Open circle at 4, shaded left

x < 4 means 4 is not included (open circle) and values are less than 4 (shaded left).

Sentence starter

I know ___ because ___.

Goal: I can explain my graph using the words number line, open circle, closed circle, and solution set.