Question 9 of 40intermediate🔧 ApplyNumerical2 marks

Solve the inequality for real xx: x+x2+x3<11x + \frac{x}{2} + \frac{x}{3} < 11

Correct Answer

x < 6, i.e., all real numbers x which are less than 6. Therefore, the solution set is x ∈ (-∞, 6).

Exercise: EXERCISE 5.1 | Q: 9 | (Page Page 7)
For More Understanding

Explanation

This is Exercise 5.1, Question 9. The student needs to solve a linear inequality with fractional coefficients. The key steps are: (1) combine like terms by finding a common denominator, (2) simplify the inequality, and (3) isolate x. Following the pattern from Examples 2-6 in the context, the solution should be expressed both as an inequality and in interval notation.

Solution Steps

  1. Step 1: Write the given inequality: x + x/2 + x/3 < 11

  2. Step 2: Find the LCM of denominators 1, 2, 3 which is 6, and combine terms: (6x + 3x + 2x)/6 < 11

  3. Step 3: Simplify the numerator: 11x/6 < 11

  4. Step 4: Multiply both sides by 6: 11x < 66

  5. Step 5: Divide both sides by 11: x < 6

  6. Step 6: The solution set is all real numbers less than 6, i.e., x ∈ (-∞, 6)

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