Writing and Graphing Inequalities Quiz

Grade 6 · Math · Quiz

Practice solving and interpreting inequalities.

Questions

1. Which symbol means 'less than or equal to'?

   1. ≤
   2. ≥
   3. <
   4. >
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   Answer: ≤

   ≤ means less than OR equal to. ≥ is greater than or equal to, < is strictly less than, > is strictly greater than.

2. x = 5 is a solution to x ≥ 5.

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   Answer: True

   x ≥ 5 includes x = 5 itself (the closed circle/equal to part). So yes, x=5 is a solution.

3. Solve: x − 3 > 9

   1. x > 12
   2. x > 6
   3. x < 12
   4. x < 6
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   Answer: x > 12

   Add 3 to both sides: x − 3 + 3 > 9 + 3 → x > 12.

4. 'No more than 20' written as an inequality using x is x ___ 20.

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   Answer: ≤

   'No more than 20' means at most 20, which is x ≤ 20 (x can equal 20 or be less).

5. Which value is NOT a solution to x < 4?

   1. 4
   2. 3
   3. 0
   4. −2
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   Answer: 4

   x < 4 means x must be strictly LESS than 4. x = 4 is not less than 4, so it is not a solution.

6. An open circle on a number line means the boundary value is included.

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   Answer: False

   Open circle means the boundary is NOT included. Closed circle means it IS included.

7. What does x ≥ −3 look like on a number line?

   1. Closed circle at −3, shaded right
   2. Open circle at −3, shaded left
   3. Closed circle at −3, shaded left
   4. Open circle at −3, shaded right
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   Answer: Closed circle at −3, shaded right

   ≥ uses a closed circle (−3 is included). Shading goes right for 'greater than.'

8. Solve: 2x ≤ 14. The solution is x ≤ ___.

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   Answer: 7

   Divide both sides by 2: 2x ÷ 2 ≤ 14 ÷ 2 → x ≤ 7.

9. A roller coaster requires riders to be at least 52 inches tall. Which inequality represents this?

   1. h ≥ 52
   2. h > 52
   3. h ≤ 52
   4. h < 52
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   Answer: h ≥ 52

   'At least 52 inches' means height must be 52 or more → h ≥ 52.

10. Which values make x + 2 ≤ 5 true? Select all that apply.

    1. x = 3 and x = 1
    2. x = 4 and x = 5
    3. x = 3 and x = 4
    4. x = 4 and x = 0
    Show answer

    Answer: x = 3 and x = 1

    x + 2 ≤ 5 → x ≤ 3. Both x=3 and x=1 satisfy x ≤ 3. (x=4 and x=5 do not.)

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