#### Answer

$x=12$

#### Work Step by Step

Multiply $6$ to both sides of the equation to obtain:
$6(0.5x+\frac{4}{3}x=6(x+10)$
Distribute $6$ to obtain:
$6(0.5x)+6(\frac{4}{3}x)=6(x) + 6(10)
\\3x+8x=6x+60
\\11x=6x+60$
Subtract $6x$ to both sides:
$11x-6x=6x+60-6x
\\5x=60$
Divide $5$ to both sides:
$\dfrac{5x}{5} = \dfrac{60}{5}
\\x=12$