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Algebraic Inequalities Practice Questions (page 2)

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Updated on Oct 3, 2011

Practice 2

  1. Add 4 to each part of the inequality:

    0 < x – 4 ≤ 4

    4 < x ≤ 8

    Because x is greater than 4, 4 is not part of the solution set, and because x is less than or equal to 8, 8 is part of the solution set. Draw a hollow circle around 4 and a closed circle around 8. Shade the area between them:

    Algebraic Inequalities

  2. Divide by –7 and change the inequality symbols from greater than to less than:

    49 > –7x > –21

    –7 < x < 3

    Because x is greater than –7, –7 is not part of the solution set, and because x is less 3, 3 is not part of the solution set. Draw a hollow circle around –7 and a hollow circle around 3. Shade the area between them:

    Algebraic Inequalities

  3. Add 7 to each part of the inequality and divide by 3:

    –13 ≤ 3x – 7 < 20

    –6 ≤ 3x < 27

    –2 ≤ x < 9

    Because x is greater than or equal to –2, –2 is part of the solution set, and because x is less than 9, 9 is not part of the solution set. Draw a closed circle around –2 and a hollow circle around 9. Shade the area between them:

    Algebraic Inequalities

  4. Subtract 1 from each part of the inequality and multiply by 5:

    0 ≥ x ≥ –10

    Because x is less than or equal to 0, 0 is part of the solution set, and because x is greater than or equal to –10, –10 is part of the solution set. Draw a closed circle around 0 and a closed circle around –10. Shade thearea between them:

    Algebraic Inequalities

  5. Add 5 to each part of the inequality and multiply by –2. Change the inequality symbols from greater than and greater than or equal to to less than and less than or equal:

    –8 < x ≤ –4

    Because x is greater than –8, –8 is not part of the solution set, and because x is less than or equal to –4, –4 is part of the solution set. Draw a hollow circle around –8 and a closed circle around –4. Shade the area between them:

    Algebraic Inequalities

Practice 3

1. Add 4 to both sides of the inequality:
      y – 4 > x
      y > x + 4
2. Add 2x to both sides of the inequality and divide by 8:
      8y – 2x ≤ 24
      8y ≤ 2x + 24
3. Subtract 15x from both sides of the equation. Divide by –5 and change the inequality symbol from greater than to less than:
      15x – 5y > 100
      –5y > 100 – 15x
      y < –20 + 3x
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