If \(\frac{x}{2}-\frac{4\left(\frac{15}{2}-\frac{x}{3}\right)}{3}=-\frac{x}{18}\), then the value of x is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 10
Simplify the bracketed term first, then multiply the whole equation by 18, the LCM of the denominators 2, 9 and 18, to clear the fractions.
The second term on the left: \(\displaystyle \frac{4}{3}\left(\frac{15}{2}-\frac{x}{3}\right)=10-\frac{4x}{9}\)
The equation becomes \(\displaystyle \frac{x}{2}-10+\frac{4x}{9}=-\frac{x}{18}\)
Multiplied by 18: \(9x-180+8x=-x\)
\(18x=180\), so \(x=10\)