Question

Solve for x:
$\frac{x+5}{6}-\frac{x+1}{9}=\frac{x+3}{4}$

• A. $-\frac{2}{7}$
• B. $-\frac{1}{7}$
• C. 7
• D. $-\frac{5}{7}$

Answer 1

The correct option is

B

$-\frac{1}{7}$

Given,
$\frac{x+5}{6}-\frac{x+1}{9}=\frac{x+3}{4}$
Multiplying both sides by 36 (LCM of 4, 6 and 9), we get,

$(\frac{x+5}{6}\times 36)-(\frac{x+1}{9}\times 36)=(\frac{x+3}{4}\times 36)$
$\Rightarrow 6(x+5)–4(x+1)=9(x+3)$
$\Rightarrow 6x+30–4x-4=9x+27$
$\Rightarrow 2x+26=9x+27$
Transposing 9x from RHS to LHS, and 26 from LHS to RHS, we get,
$2x-9x=27-26$
$\Rightarrow -7x=1$
Dividing both sides by -7, we get,
$x=-\frac{1}{7}$