Question 30 of 40intermediate🔧 ApplyNumerical2 marks

Solve the inequality: −15<3(x−2)5≤0-15 < \frac{3(x-2)}{5} \leq 0

Correct Answer

x ∈ (-23, 2]

Exercise: Miscellaneous Exercise on Chapter 5 | Q: 4 | (Page Page 10)
For More Understanding

Explanation

The inequality is solved by applying the rules of inequalities: multiplying/dividing by positive numbers does not change the inequality sign (Rule 2), and adding the same number to all parts preserves the inequality (Rule 1). The compound inequality is broken into two parts and solved step by step, resulting in the interval (-23, 2].

Solution Steps

  1. Step 1: Multiply the inequality by 5 (positive): -75 < 3(x-2) ≤\leq 0.

  2. Step 2: Divide by 3 (positive): -25 < x-2 ≤\leq 0.

  3. Step 3: Add 2 to all parts: -23 < x ≤\leq 2.

  4. Step 4: Hence, the solution set is x ∈ (-23, 2].

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