Solving Linear Inequalities and Solution Sets · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Solving Linear Inequalities and Solution Sets

Mathematics · Algebra · ages 15-16
Name ______________________   Date ____________

  1. Solve 5x - 4 < 16. What is the largest whole number in the solution set?

    Answer: ______________

  2. Adding a number to both sides of an inequality changes the direction of the sign.

    Circle one:   True   False

  3. Solve 3(x - 2) < 12.

    • x < 6
    • x < 10
    • x > 6
    • x < 2

  4. Solve 2x + 5 > 11. What is the solution?

    • x is greater than 6
    • x is less than 3
    • x is greater than 3
    • x is greater than 8

  5. How many integers satisfy -3 < 2x + 1 ≤ 7?

    Answer: ______________

  6. The inequality -x <= 4 has the solution x >= -4.

    Circle one:   True   False

  7. Sam solves 10 - 4x <= 2 and writes x <= 2. Where is the slip?

    • He should have added 10 instead of subtracting
    • He divided by 4 instead of -4
    • He subtracted 8 instead of 10
    • He forgot to flip the sign when dividing by -4

  8. Solve 1 < 2x - 3 <= 5. How many whole numbers are in the solution set?

    Answer: ______________

  9. Which value is in the solution set of x < -2 or x >= 5?

    • -2
    • 3
    • 0
    • 5

  10. Solve -5 < 3x + 2 <= 7. How many whole numbers are in the solution set?

    Answer: ______________

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Answer key

For grown-ups. Fold this page away before handing over the rest.

Solving Linear Inequalities and Solution Sets W1-mt_QkG3Cw5VgM-s1

  1. 3 · Add 4 to get 5x < 20, so x < 4, and the largest whole number below 4 is 3.
  2. False · Adding or subtracting the same number from both sides keeps the order the same, so the sign does not change.
  3. x < 6 · Expand to 3x - 6 < 12, so 3x < 18 and x < 6.
  4. x is greater than 3 · Subtract 5 from both sides to get 2x > 6, then divide by 2 to get x > 3.
  5. 5 · The integers are -1, 0, 1, 2, 3, which are 5 in total.
  6. True · Multiply by -1 and flip the sign: x >= -4.
  7. He forgot to flip the sign when dividing by -4 · Subtracting 10 gives -4x <= -8, and dividing by -4 flips the sign, so the correct answer is x >= 2, not x <= 2.
  8. 2 · Add 3 to get 4 < 2x <= 8, divide by 2 to get 2 < x <= 4, and the whole numbers are 3 and 4.
  9. 5 · The set is x < -2 or x >= 5, so 5 is included (the or-equal end) but -2, 3 and 0 are not.
  10. 4 · Subtract 2 to get -7 < 3x <= 5, divide by 3 to get -7/3 < x <= 5/3, about -2.33 < x <= 1.67, and the whole numbers are -2, -1, 0 and 1.
Worksheet · LightMySky