Question

Solve for $x$

$\frac{(2+x)(7-x)}{(5-x)(4+x)}=1$

• A. $\frac{3}{2}$
• B. $\frac{1}{2}$
• C. $\frac{5}{2}$
• D. $\frac{7}{2}$

Answer 1

The correct option is A $\frac{3}{2}$

$\frac{(2+x)(7-x)}{(5-x)(4+x)}=1$

$\Rightarrow (2+x)(7-x)=(5-x)(4+x)$

$\Rightarrow 14-2x+7x-x^2=20+5x-4x-x^2$

$\Rightarrow 14+5x=20+x$

$\Rightarrow 5x-x=20-14=6$

$\Rightarrow 4x=6$

$\Rightarrow x=\frac{6}{4}=\frac{3}{2}$

Thus, the solution of the given equation is $x=\frac{3}{2}$