Compound inequalities: "and" and "or"

Answer Key - Grade 9 Math Worksheet

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

1. 1.

   Ari solves 3 < 2x + 1 < 11 on paper. What is the answer, written like 2 < x < 9 with the smaller number first?

   1 < x < 5
2. 2.

   Bo solves -4 ≤ 2x - 2 < 6 with a pencil. What is the answer, written like 2 < x < 9 with the smaller number first?

   -1 ≤ x < 4
3. 3.

   Kira solves x + 3 < 1 or 2x > 10 on paper. What is the answer, written like x < 1 or x > 6 with the left piece first?

   x < -2 or x > 5
4. 4.

   Luz solves 2x - 1 ≤ -5 or x - 4 ≥ 1 with a pencil. What is the answer, written like x < 1 or x > 6 with the left piece first?

   x ≤ -2 or x ≥ 5
5. 5.

   Milo solves 3x < -9 or x - 2 > 6 in a math notebook. What is the answer, written like x < 1 or x > 6 with the left piece first?

   x < -3 or x > 8
6. 6.

   Noah solves 2x ≤ -8 or x + 4 > 9 on paper. What is the answer, written like x < 1 or x > 6 with the left piece first?

   x ≤ -4 or x > 5
7. 7.

   The greenhouse must stay at least 18 degrees and under 25 degrees. Pia writes an inequality for t. Which one is right?

   • 18 ≤ t < 25
   • 18 ≤ t ≤ 25
   • 18 < t ≤ 25
   • t ≥ 18 or t < 25
8. 8.

   A school backpack must weigh more than 2 kilograms and at most 6 kilograms. Ren writes an inequality for w. Which one is right?

   • w > 2 or w ≤ 6
   • 2 ≤ w < 6
   • 2 < w ≤ 6
   • 2 ≤ w ≤ 6
9. 9.

   Esme solves x ≥ 7 and x ≤ 3 in a math notebook. Which answer is right?

   • No solution
   • x ≥ 7
   • 3 ≤ x ≤ 7
   • All real numbers
10. 10.

    Luz wants to graph x < -4 or x ≥ 3 with a pencil. Which graph is right?

    • Open circle at -4 shaded left, closed circle at 3 shaded right
    • Open circle at -4, closed circle at 3, shaded between
    • Closed circles at -4 and 3, shaded outward
    • Closed circle at -4 shaded left, open circle at 3 shaded right