Course Glossary

Solving Multi-Step Linear Inequalities Algebraically

Pencils

Problem SetUsing your knowledge of multi-step linear inequalities, solve each problem shown below. Follow the instructions for each portion, answer all of the questions, and make sure to show all of your work.

This activity is available below or in a printable document.

For problems 1–5: Solve for x. Show detailed work. Write your solution using set notation, and graph the solution set.

  1. 7 − 4(x + 3) < 11

  2. 4 / 5
    x − 1 > 19

  3. 11x + 2 ≤ 5(2x − 3)

  4. 9x − 2 ≥ 3x + 8

  5. 4(1 + 2x) + 5 ≤ − 15

For problems 6 and 7: Apply your knowledge of the properties of inequality to answer each question.

  • Step 1:
    3 / 4
    x + 2 < 8
  • Step 2:
    3 / 4
    x + 2 − 2 < 8 − 2
  • Step 3:
    3 / 4
    x < 6
  • Step 4: 4 ·
    3 / 4
    x < 6 · 4
  • Step 5: 3x < 24
  • Step 6:
    3x / 3
    <
    24 / 3
  • Step 7: x < 8
  1. Which property justifies the work between...
    1. Step 1 and Step 2?
    2. Step 3 and Step 4?
    3. Step 5 and Step 6?

  2. Which property justifies the work below?
    If 9y + 4 < x, and x < 5y, then 9y + 4 < 5y.

Assignment
Once you have completed this assignment, please submit your work to the dropbox.