Find the range of values of x which satisfy the inequality \(\frac{x}{2}\) + \(\frac{x}{3}\) + \(\frac{x}{4}\) < 1

  • A x < \(\frac{12}{13}\)
  • B x < 13
  • C x < 9
  • D \(\frac{13}{12}\)
jamb 1991mathematics

The correct answer is A. x < \(\frac{12}{13}\)

To solve the inequality \(\frac{x}{2} + \frac{x}{3} + \frac{x}{4} < 1\), we need to find a common denominator for the fractions, which is 12. Multiply each term by 12 to get rid of the fractions:

\(6x + 4x + 3x < 12\)

Combine like terms:

13x < 12

Now, divide by 13 to solve for x:

\(x < \frac{12}{13}\)

So, the correct answer is \(x < \frac{12}{13}\).

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