CORE_MATH • SHS 1Term 2WAEC / WASSCE SyllabusVIP Lesson
Linear Inequalities in One Variable & Number Line
Solving linear inequalities, the sign reversal rule, combined inequalities, and graphing solution sets on the real number line.
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Real-World Context & Relevance in Ghana
Ghana National Petroleum Authority sets fuel price ceiling bands using compound inequalities to ensure fair retail pricing while preventing consumer exploitation.
Key Syllabus Learning Objectives
- 1Solve single-step and multi-step linear inequalities
- 2Apply the sign reversal rule correctly when dividing by negative numbers
- 3Solve compound inequalities and express solution sets in interval and set-builder notation
- 4Graph inequality solution sets on a real number line with proper circle conventions
1
The Sign Reversal Principle
Consider 4 > 2. If we multiply both sides by -1, we get -4 and -2. Clearly, -4 is LESS than -2 (-4 < -2). Hence, multiplying or dividing by a negative number inverts the order relation.
- Check the coefficient of x before dividing.
- If negative, flip the symbol immediately (< becomes >, ≥ becomes ≤).
- If positive, the inequality symbol stays identical.
Core Takeaway:
Always reverse the inequality symbol when dividing or multiplying by a negative number.
WAEC / WASSCE Examiner Tips
- When graphing on a number line, ensure circles are clearly open (○) or shaded (●). WAEC deducts B1 marks for ambiguous circles.
- If asked for "the smallest integer satisfying...", list values to find the exact boundary integer.
- Use a ruler to draw neat number lines with evenly spaced tick marks.
Common Candidate Pitfalls & Errors to Avoid
- Forgetting to reverse the inequality sign when dividing by a negative number.
- Using solid dots for strict inequalities (<, >).
- Confusing the directions of < and > on negative coordinates.
Topic Mastery Checklist
- Can I solve -3x + 5 ≤ 14?
- Can I solve -2 < 3x + 1 ≤ 10?
- Can I draw the solution set on a number line accurately?
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