Inequality Solutions Lecture Notes

Problem Statement

• Inequality to solve: 3l - 6 ≥ 8
• Objective: Describe the solutions in terms of l.

Steps to Solve the Inequality

1. Isolate the term involving l:

   • Start with: 3l - 6 ≥ 8
   • Add 6 to both sides:
     • 3l - 6 + 6 ≥ 8 + 6
     • Simplifies to: 3l ≥ 14

2. Divide by the coefficient of l:

   • Divide both sides by 3:
     • (3l)/3 ≥ 14/3
     • Simplifies to: l ≥ 14/3

Key Points

• Adding 6 cancels out the -6 on the left side.
• Dividing by a positive number (3) does not change the direction of the inequality.
• Important to note: If dividing by a negative number, you would reverse the inequality sign.

Final Solution

• The solution to the inequality is:
  l ≥ 14/3
• This corresponds to the given choice in the options.