Match the inequalities to the correct column. When graphing them on a number line, would you use an open dot or a closed dot? Use the chart below for reference.

Question

x>8

y<-2

j geq -1

b leq 12

Answer 1

Here’s how to categorize the inequalities and whether to use an open dot or a closed dot when graphing them on a number line:

Column 1: Inequalities that use an open dot

• x > 8: This inequality means that x can be any number greater than 8, but not equal to 8. Therefore, it uses an open dot at 8.
• y < -2: This means that y can be any number less than -2, but not equal to -2. It also uses an open dot at -2.

Column 2: Inequalities that use a closed dot

• j ≥ -1: This inequality means that j can be equal to -1 or any number greater than -1. Therefore, it uses a closed dot at -1.
• b ≤ 12: This means that b can be equal to 12 or any number less than 12. This also uses a closed dot at 12.

Summary

• Open Dot:

  • x > 8
  • y < -2

• Closed Dot:

  • j ≥ -1
  • b ≤ 12