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 6 - 2x < 0. What is the boundary value of the solution?

    Answer: ______________

  2. The solution x >= 2 is shown on a number line with which endpoint?

    • an open circle at 2, shaded right
    • a closed circle at 2, shaded left
    • an open circle at 2, shaded left
    • a closed circle at 2, shaded right

  3. Solve 4x + 3 > 19. What is the solution?

    • x is greater than 4
    • x is greater than 16
    • x is greater than 7
    • x is greater than 22

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

    Circle one:   True   False

  5. Solve 2(x + 1) > 8. What is the solution?

    • x is greater than 3
    • x is greater than 4
    • x is less than 3
    • x is greater than 5

  6. Solve 2 < x + 4 <= 9. What is the solution?

    • x is greater than 2 and at most 5
    • x is greater than -2 and at most 5
    • x is greater than -2 and at most 13
    • x is greater than -6 and at most 5

  7. Solve -x + 3 > -1. What is the solution?

    • x is less than 4
    • x is greater than 4
    • x is less than -4
    • x is greater than -4

  8. Solve -2 < 3x + 1 <= 7. How many whole numbers are in the solution set?

    Answer: ______________

  9. Solve 3 - 2x <= -1 < 5 - 2x. What is the solution?

    • x is at least 2 and less than 3
    • x is at most 2
    • x is greater than 2 and at most 4
    • x is at least 2 and less than 4

  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 · Subtract 6 to get -2x < -6, divide by -2 and flip the sign to get x > 3, so the boundary is 3.
  2. a closed circle at 2, shaded right · The sign is greater than or equal to, so the endpoint 2 is included (a closed circle) and the solution runs to the right.
  3. x is greater than 4 · Subtract 3 to get 4x > 16, then divide by 4 to get x > 4.
  4. False · Adding or subtracting the same number from both sides keeps the order the same, so the sign does not change.
  5. x is greater than 3 · Expand the bracket first: 2x + 2 > 8. Subtract 2 to get 2x > 6, then divide by 2: x > 3.
  6. x is greater than -2 and at most 5 · Subtract 4 from all three parts: 2 - 4 < x <= 9 - 4, so -2 < x <= 5.
  7. x is less than 4 · Subtract 3 to get -x > -4, then multiply by -1 and flip the sign to get x < 4.
  8. 3 · Subtract 1 to get -3 < 3x <= 6, divide by 3 to get -1 < x <= 2, and the whole numbers are 0, 1, 2.
  9. x is at least 2 and less than 3 · The left part 3 - 2x <= -1 gives x >= 2, and the right part -1 < 5 - 2x gives x < 3, so combining gives 2 <= x < 3.
  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