Inequalities with number lines
key notes:
Number Line:
a visual representation of numbers arranged in order, with smaller numbers to the left and larger numbers to the right
Understanding Inequalities:
- A filled-in circle includes the number it is located on.
- An open circle does not include the number it is located on.
Learn with an example
▶️ Which number line shows the numbers that are less than or equal to 1?
- Look at the first number line.
The number line has a filled-in circle on 1. That means the inequality includes the number 1.
The number line also shows an arrow pointing to the left, where numbers are less than 1. That means the inequality also includes numbers less than 1.
Together, the circle and arrow show less than or equal to 1. This is the correct number line.
Now look at the second number line.
The number line has an open circle on 1. That means the inequality does not include the number 1.
The number line also shows an arrow pointing to the left, where numbers are less than 1. That means the inequality includes numbers less than 1.
Together, the circle and arrow show less than 1. This is not the correct number line.
▶️ Which number line shows the numbers that are less than 7?
- Look at the first number line.
The number line has an open circle on 7. That means the inequality does not include the number 7.
The number line also shows an arrow pointing to the left, where numbers are less than 7. That means the inequality includes numbers less than 7.
Together, the circle and arrow show less than 7. This is the correct number line.
Now look at the second number line.
The number line has an open circle on 8. That means the inequality does not include the number 8.
The number line also shows an arrow pointing to the left, where numbers are less than 8. That means the inequality includes numbers less than 8.
Together, the circle and arrow show less than 8. This is not the correct number line.
🗼 Which inequality does this number line show?
- greater than or equal to 2
- less than or equal to 3
- less than or equal to 4
- less than 3
- The number line has an open circle on 3. That means the inequality does not include the number 3.
- The number line also shows an arrow pointing to the left, where numbers are less than 3. That means the inequality includes numbers less than 3.
- Together, the circle and arrow show less than 3.
Let’s practice!
