Question 7 of 40beginner🔧 ApplyNumerical2 marks

Solve the inequality for real xx: 3(x−1)≤2(x−3)3(x - 1) \leq 2(x - 3)

Correct Answer

x ∈ (-∞, -3]

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

Explanation

This is a linear inequality problem from Exercise 5.1, Question 7. The student needs to solve for real x by first expanding the brackets, then collecting like terms, and finally isolating x. The key steps involve applying Rule 1 (adding/subtracting equal numbers from both sides) and being careful with the inequality sign. Since the coefficient of x turns out to be positive (1), the inequality sign remains unchanged.

Solution Steps

  1. Step 1: Expand both sides: 3(x - 1) ≤\leq 2(x - 3) becomes 3x - 3 ≤\leq 2x - 6

  2. Step 2: Subtract 2x from both sides (Rule 1): 3x - 2x - 3 ≤\leq 2x - 2x - 6 which gives x - 3 ≤\leq -6

  3. Step 3: Add 3 to both sides (Rule 1): x - 3 + 3 ≤\leq -6 + 3 which gives x ≤\leq -3

  4. Step 4: Write the solution set: Since x is a real number, all real numbers less than or equal to -3 are solutions. Therefore, x ∈ (-∞, -3]

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