Answer
$x=3$
Work Step by Step
Multiply both sides by the LCD (which is 28) to obtain:
$\require{cancel}
28 \left(\dfrac{2+5x}{4}\right)=28\left(\dfrac{11}{28}+\dfrac{8x+3}{7}\right)
\\\cancel{28}7 \left(\dfrac{2+5x}{\cancel{4}}\right)=28\left(\dfrac{11}{28}\right)+28\left(\dfrac{8x+3}{7}\right)
\\7(2+5x)=\cancel{28}\left(\dfrac{11}{\cancel{28}}\right)+\cancel{28}4\left(\dfrac{8x+3}{\cancel{7}}\right)
\\7(2+5x)=11+4(8x+3)$
Distribute $7$ on the left side and $4$ on the right side of the equation to obtain:
$7(2)+7(5x)=11+4(8x)+4(3)
\\14+35x=11+32x+12
\\35x+14=32x+23$
Subtract $32x$ and $14$ to both sides of the equation:
$35x+14-32x-14=32x+23-32x-14
\\3x=9$
Divide 3 to both sides:
$\frac{3x}{3}=\frac{9}{3}
\\x=3$
