Compound inequalities: "and" and "or"

Answer Key - Grade 9 Math Worksheet

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

1. 1.

   Esme solves 5 < x + 2 ≤ 9 in a math notebook. What is the answer, written like 2 < x < 9 with the smaller number first?

   3 < x ≤ 7
2. 2.

   Jun solves 2 ≤ 4x - 6 ≤ 14 on paper. What is the answer, written like 2 < x < 9 with the smaller number first?

   2 ≤ x ≤ 5
3. 3.

   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
4. 4.

   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
5. 5.

   Swim practice is canceled when the water is colder than 16 degrees or warmer than 30 degrees. Tala writes an inequality for t. Which one is right?

   • 16 < t < 30
   • t ≤ 16 or t ≥ 30
   • t < 16 and t > 30
   • t < 16 or t > 30
6. 6.

   A phone beeps when the charge is at most 10 percent or at least 90 percent. Zee writes an inequality for c. Which one is right?

   • 10 ≤ c ≤ 90
   • c ≤ 10 and c ≥ 90
   • c ≤ 10 or c ≥ 90
   • c < 10 or c > 90
7. 7.

   Ari solves x > 5 and x < 2 on paper. Which answer is right?

   • 2 < x < 5
   • x > 5
   • All real numbers
   • No solution
8. 8.

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

   • 3 ≤ x ≤ 7
   • x ≥ 7
   • All real numbers
   • No solution
9. 9.

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

   • Open circle at -4, closed circle at 3, shaded between
   • Closed circles at -4 and 3, shaded outward
   • Open circle at -4 shaded left, closed circle at 3 shaded right
   • Closed circle at -4 shaded left, open circle at 3 shaded right
10. 10.

    Milo wants to graph 2 ≤ x < 9 in a math notebook. Which graph is right?

    • Open circles at 2 and 9, shaded between
    • Closed circle at 2, open circle at 9, shaded between
    • Open circle at 2, closed circle at 9, shaded between
    • Closed circle at 2 shaded left, open circle at 9 shaded right