Question 10 of 40intermediate🔧 ApplyNumerical2 marks

Solve the inequality for real xx: x3>x2+1\frac{x}{3} > \frac{x}{2} + 1

Correct Answer

x ∈ (-∞, -6)

Exercise: EXERCISE 5.1 | Q: 10 | (Page Page 7)
For More Understanding

Explanation

This question tests the student's understanding of solving linear inequalities. The key steps involve rearranging terms, combining fractions, and applying Rule 2 correctly when multiplying/dividing by negative numbers. The context provides clear examples (Examples 3 and 4) showing how to handle sign reversal and express final answers in interval notation.

Solution Steps

  1. Step 1: Given inequality is x/3 > x/2 + 1

  2. Step 2: Subtract x/2 from both sides (Rule 1): x/3 - x/2 > 1

  3. Step 3: Simplify LHS: (2x - 3x)/6 > 1 or -x/6 > 1

  4. Step 4: Multiply both sides by 6 (Rule 2 - positive number): -x > 6

  5. Step 5: Multiply both sides by -1 (Rule 2 - negative number reverses inequality): x < -6

  6. Step 6: Solution set is x ∈ (-∞, -6)

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