Question 28 of 40intermediate🔧 ApplyNumerical2 marks

Solve the inequality: 6≤−3(2x−4)<126 \leq -3 (2x - 4) < 12

Correct Answer

The solution is 0<x≤10 < x \leq 1, i.e., x∈(0,1]x \in (0, 1] for real numbers. For integers, the solution set is {1}\{1\}.

Exercise: Miscellaneous Exercise on Chapter 5 | Q: 2 | (Page Page 10)
For More Understanding

Explanation

This question tests solving compound inequalities. Following the method shown in Example 9 and Example 10 from the context, we solve the inequality simultaneously by applying operations to all parts. The key steps involve expanding, then subtracting constants, and finally dividing by a negative number (which reverses the inequality signs).

Solution Steps

  1. Step 1: Expand the inequality

    6≤−3(2x−4)<126 \leq -3(2x - 4) < 12 6≤−6x+12<126 \leq -6x + 12 < 12

  2. Step 2: Subtract 12 from all parts

    6−12≤−6x+12−12<12−126 - 12 \leq -6x + 12 - 12 < 12 - 12 −6≤−6x<0-6 \leq -6x < 0

  3. Step 3: Divide by -6 and reverse inequality signs

    −6−6≥x>0−6\frac{-6}{-6} \geq x > \frac{0}{-6} 1≥x>01 \geq x > 0

  4. Step 4: Write in standard form

    0<x≤10 < x \leq 1

    For real numbers: x∈(0,1]x \in (0, 1] For integers: Solution set is {1}\{1\}

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