Question 29 of 40intermediate🔧 ApplyNumerical2 marks

Solve the inequality: −3≤4−7x2≤18-3 \leq 4 - \frac{7x}{2} \leq 18

Correct Answer

The solution set is x∈[−4,2]x \in [-4, 2] or −4≤x≤2-4 \leq x \leq 2.

Exercise: Miscellaneous Exercise on Chapter 5 | Q: 3 | (Page Page 10)
For More Understanding

Explanation

This is a double inequality problem similar to Example 10 in the Miscellaneous Examples section. The key steps involve eliminating the fraction by multiplying throughout, then isolating x. When dividing by a negative number, the inequality signs must be reversed.

Solution Steps

  1. Step 1: Given inequality: −3≤4−7x2≤18-3 \leq 4 - \frac{7x}{2} \leq 18

  2. Step 2: Multiply all parts by 2 to eliminate denominator: −6≤8−7x≤36-6 \leq 8 - 7x \leq 36

  3. Step 3: Subtract 8 from all parts: −14≤−7x≤28-14 \leq -7x \leq 28

  4. Step 4: Divide by -7 and reverse inequality signs: 2≥x≥−42 \geq x \geq -4

  5. Step 5: Rewrite in standard form: −4≤x≤2-4 \leq x \leq 2

  6. Step 6: Solution set is x∈[−4,2]x \in [-4, 2]

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