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.

   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
4. 4.

   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
5. 5.

   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
6. 6.

   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
7. 7.

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

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

   Bo solves x < 5 or x > 2 with a pencil. Which answer is right?

   • No solution
   • x < 2 or x > 5
   • 2 < x < 5
   • All real numbers
9. 9.

   Kira wants to graph -1 < x ≤ 3 on paper. Which graph is right?

   • Open circle at -1 shaded left, closed circle at 3 shaded right
   • Open circles at -1 and 3, shaded between
   • Open circle at -1, closed circle at 3, shaded between
   • Closed circle at -1, open circle at 3, shaded between
10. 10.

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

    • Closed circle at -4 shaded left, open circle at 3 shaded 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