Question 31 of 40intermediate🔧 ApplyNumerical2 marks

Solve the inequality: −12<4−3x−5≤2-12 < 4 - \frac{3x}{-5} \leq 2

Correct Answer

The solution set is x ∈ (-80/3, -10/3].

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

Explanation

This question tests solving a compound inequality with a negative denominator. Following the method in Example 10 from the textbook, we solve the inequality by applying operations to all three parts simultaneously. The key step is recognizing that -3x/-5 simplifies to +3x/5, and then systematically isolating x through subtraction and multiplication operations.

Solution Steps

  1. Step 1: Simplify the inequality: -12 < 4 - (3x/-5) ≤\leq 2 becomes -12 < 4 + 3x/5 ≤\leq 2

  2. Step 2: Subtract 4 from all parts: -16 < 3x/5 ≤\leq -2

  3. Step 3: Multiply by 5: -80 < 3x ≤\leq -10

  4. Step 4: Divide by 3: -80/3 < x ≤\leq -10/3

  5. Step 5: Solution set is x ∈ (-80/3, -10/3]

PreviousNext