Linear Inequalities and Absolute Value Quiz

Grade 10 · Math · Quiz

Test your skills solving and graphing inequalities and absolute value problems.

Questions

1. Solve: 2x - 3 ≥ 7. What is x?

   1. x ≥ 5
   2. x ≤ 5
   3. x ≥ 2
   4. x ≤ 2
   Show answer

   Answer: x ≥ 5

   2x-3≥7 → 2x≥10 → x≥5. No sign flip because we divide by positive 2.

2. The solution to |x| = -3 has two solutions: x = 3 and x = -3.

   Show answer

   Answer: False

   Absolute value is always ≥ 0. |x| = -3 has NO solution — you can't have a distance of negative 3.

3. Solve: -2x < 8. The solution is x > ___.

   Show answer

   Answer: -4

   Divide by -2 and flip: -2x < 8 → x > -4. Flip because dividing by negative.

4. Which graph represents x ≤ 3?

   1. Open circle at 3, arrow pointing right
   2. Closed circle at 3, arrow pointing left
   3. Open circle at 3, arrow pointing left
   4. Closed circle at 3, arrow pointing right
   Show answer

   Answer: Closed circle at 3, arrow pointing left

   x ≤ 3 uses ≤, so the endpoint 3 IS included (closed circle), and values go left (decreasing).

5. Solve |x + 2| = 6. The solutions are:

   1. x = 4 only
   2. x = 8 or x = -4
   3. x = 4 or x = -8
   4. x = 8 only
   Show answer

   Answer: x = 4 or x = -8

   Split: x+2=6 → x=4; and x+2=-6 → x=-8. Solutions: x=4 or x=-8.

6. The solution to |2x - 1| < 5 is -2 < x < 3.

   Show answer

   Answer: True

   |2x-1|<5 → -5<2x-1<5 → -4<2x<6 → -2<x<3. Correct.

7. The absolute value |−15| = ___.

   Show answer

   Answer: 15

   Absolute value gives the distance from zero; |-15| = 15 regardless of the negative sign.

8. Which inequality has no solution?

   1. x + 2 > 0
   2. |x| > -5
   3. |x| < -3
   4. 2x ≥ -4
   Show answer

   Answer: |x| < -3

   |x| is always ≥ 0, so |x| < -3 is impossible — no value of x satisfies it. This is the empty solution set.

9. x > 3 OR x < -1 represents values either to the right of 3 or to the left of -1 on the number line.

   Show answer

   Answer: True

   'Or' inequalities create a union — all values satisfying either condition. This graphs as two rays pointing away from each other.

10. A compound inequality 1 < x ≤ 5 means:

    1. x is greater than 1 only
    2. x is greater than 1 AND at most 5
    3. x is at least 1 and less than 5
    4. x equals 1 through 5 integers only
    Show answer

    Answer: x is greater than 1 AND at most 5

    1 < x ≤ 5 is a compound 'and' inequality: x must be strictly greater than 1 AND less than or equal to 5.

Get a personalized course on Linear Inequalities and Absolute Value built around your child.