Write and graph x > c, x < c

Answer Key - Grade 6 Math Worksheet - Building Confidence

Circle the best answer, or write your answer on the line.

1. 1.

   Ari earns the hiking badge only if the miles walked, x, are more than 9. The bar for x is longer than the bar for 9. What inequality for x do the bars show?

   x > 9
2. 2.

   Jun packs a library bag that holds at most 7 books. The bar for the books, x, is as long as the bar for 7 or shorter. What inequality for x do the bars show?

   x ≤ 7
3. 3.

   Noah loads a van that can carry at most 17 boxes. The bar for the boxes, x, is as long as the bar for 17 or shorter. What inequality for x do the bars show?

   x ≤ 17
5. 4.

   Pia checks a clue: which number line shows x > 6? An open circle means the number is not a solution. A closed circle means it is.

   • an open circle at 6, shaded to the right
   • an open circle at 6, shaded to the left
   • a closed circle at 6, shaded to the right
6. 5.

   Tala checks a clue: which number line shows x < 15? An open circle means the number is not a solution. A closed circle means it is.

   Use the picture in question 4.

   • a closed circle at 15, shaded to the left
   • an open circle at 15, shaded to the right
   • an open circle at 15, shaded to the left
7. 6.

   Zee checks a clue: which number line shows x ≥ 12? An open circle means the number is not a solution. A closed circle means it is.

   Use the picture in question 4.

   • an open circle at 12, shaded to the right
   • a closed circle at 12, shaded to the right
   • a closed circle at 12, shaded to the left
8. 7.

   Ari needs a piece of yarn longer than 5 meters, so x > 5. Test these numbers in x > 5: 5.5, 6 and 20. They all work. Which statement is true?

   Use the picture in question 4.

   • Many numbers work, such as 5.5 and 6. There are infinitely many solutions.
   • Only whole numbers work: 6, 7, 8 and so on, because fractions and decimals are not allowed
   • Only one number works: 6.
9. 8.

   Bo needs a ladder shorter than 18 feet, so x < 18. Test these numbers in x < 18: 17.5, 12 and 3. They all work. Which statement is true?

   Use the picture in question 4.

   • Only one number works: 12.
   • Many numbers work, such as 17.5 and 12. There are infinitely many solutions.
   • Only whole numbers work: 17, 16, 15 and so on, because decimals cannot be solutions
10. 9.

    Esme's recipe needs at least 4 cups of oats, so x ≥ 4. Test these numbers in x ≥ 4: 4, 4.5 and 9. They all work. Which statement is true?

    Use the picture in question 4.

    • Only one number works: 4.
    • Many numbers work, such as 4.5 and 9. There are infinitely many solutions.
    • Only whole numbers work: 4, 5, 6 and so on.
11. 10.

    Jun packs a box that may weigh at most 19 pounds, so x ≤ 19. Test these numbers in x ≤ 19: 19, 18.5 and 3. They all work. Which statement is true?

    Use the picture in question 4.

    • Only whole numbers work: 19, 18, 17 and so on.
    • Only one number works: 19.
    • Many numbers work, such as 18.5 and 3. There are infinitely many solutions.