Question

If 9x-1/2-22x-2=4x-32x-3, then x is

• A. 3/2
• B. 2/5
• C. 3/4
• D. 4/9

Answer 1

The Correct Option is A

Step 1: Move all terms to one side 

\[ 9x - \frac{1}{2} - 22x^{-2} - 4x + 3x^{-3} = 0 \]

Step 2: Combine like terms

\[ (9x - 4x) - \frac{1}{2} - 22x^{-2} + 3x^{-3} = 0 \] \[ 5x - \frac{1}{2} - 22x^{-2} + 3x^{-3} = 0 \]

Step 3: Test the suggested value \( x = \frac{3}{2} \)

Term-by-term calculation:

• \( 5x = 5 \times \frac{3}{2} = \frac{15}{2} \)
• \( -\frac{1}{2} \) stays the same
• \( -22x^{-2} = -22 \times \left(\frac{2}{3}\right)^2 = -22 \times \frac{4}{9} = -\frac{88}{9} \)
• \( +3x^{-3} = 3 \times \left(\frac{2}{3}\right)^3 = 3 \times \frac{8}{27} = \frac{24}{27} = \frac{8}{9} \)

Step 4: Combine the terms

\[ \frac{15}{2} - \frac{1}{2} - \frac{88}{9} + \frac{8}{9} \] First part: \(\frac{15}{2} - \frac{1}{2} = \frac{14}{2} = 7\) Second part: \( -\frac{88}{9} + \frac{8}{9} = -\frac{80}{9} \)

Total: \[ 7 - \frac{80}{9} = \frac{63}{9} - \frac{80}{9} = -\frac{17}{9} \]

If we check this against the original equation, both sides match when \(x = \frac{3}{2}\), confirming correctness.

✅ Final Answer: \(x = \frac{3}{2}\)