Solving and Representing Linear Inequalities
This lesson covers solving and representing linear inequalities. Students will progress from simple one-step inequalities to multi-step problems involving negative coefficients and double inequalities, ensuring they understand the structural similarities and differences between equations and inequalities.
Learning objectives
- Represent inequalities on a number line using open and closed circles.
- Solve linear inequalities in one variable using inverse operations.
- Identify the set of integers that satisfy a given double inequality.
- Understand and apply the rule for reversing inequality signs when multiplying or dividing by a negative number.
Lesson plan (60 minutes)
Introduction · 5 min
Do Now: Rapid fire solving of basic one-step equations (e.g., x + 5 = 10) to refresh inverse operations.
Direct Instruction · 15 min
Teacher-led instruction: Introducing inequality symbols, representing on a number line, and the golden rule of multiplying/dividing by negatives.
Guided Practice · 10 min
Guided Practice: Solving two-step inequalities as a class using the 'I do, We do, You do' method.
Independent Practice · 20 min
Independent Practice: Students work through differentiated worksheets (Support, Core, or Stretch).
Plenary/Assessment · 10 min
Plenary: Multiple-choice quiz to check for understanding and address remaining misconceptions.
Key vocabulary
- Inequality
- A mathematical statement that two expressions are not equal, using symbols like < or >.
- Integer
- A whole number (can be positive, negative, or zero).
- Open Circle
- A circle on a number line that is not filled in, used for < and > to show the number is not included.
- Closed Circle
- A circle on a number line that is filled in, used for ≤ and ≥ to show the number is included.
- Inverse Operation
- The mathematical operation that 'undoes' another (e.g., subtraction is the inverse of addition).
Core worksheet (first questions)
- Solve: 2x + 3 > 11
- Solve: 4x - 5 ≤ 7
- Solve: 3x + 2 < 23
- Solve: (x / 4) - 1 > 2
Quiz (sample)
1. Solve: x + 5 > 9
- A. x < 4
- B. x > 4
- C. x = 4
- D. x ≥ 4
2. How is x > 3 represented on a number line?
- A. A closed circle at 3, with an arrow pointing left.
- B. An open circle at 3, with an arrow pointing left.
- C. A closed circle at 3, with an arrow pointing right.
- D. An open circle at 3, with an arrow pointing right.
3. Solve: 3x ≤ 12
- A. x ≤ 4
- B. x ≥ 4
- C. x < 4
- D. x > 4
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