Answer
$\{\frac{21}{11}\}$.
Work Step by Step
The given equation is
$\Rightarrow 2x-\frac{x-3}{8}=\frac{1}{2}+\frac{x+5}{2}$
The LCD is $8$.
Multiply the equation by $8$.
$\Rightarrow 8\cdot \left (2x-\frac{x-3}{8}\right )=8\cdot \left (\frac{1}{2}+\frac{x+5}{2}\right )$
Use the distributive property.
$\Rightarrow 8\cdot 2x-8\cdot \frac{x-3}{8}=8\cdot \frac{1}{2}+8\cdot \frac{x+5}{2}$
Simplify.
$\Rightarrow 16x- (x-3)=4+4\cdot (x+5)$
Use the distributive property.
$\Rightarrow 16x- x+3=4+4x+20$
Add like terms.
$\Rightarrow 15x+3=24+4x$
Add $-4x-3$ to both sides.
$\Rightarrow 15x+3-4x-3=24+4x-4x-3$
Simplify.
$\Rightarrow 11x=21$
Divide both sides by $11$.
$\Rightarrow \frac{11x}{11}=\frac{21}{11}$
Simplify.
$\Rightarrow x=\frac{21}{11}$
The solution set is $\{\frac{21}{11}\}$.
