#### Answer

$x=10$

#### Work Step by Step

Multiply the LCD, which is $70$, to both sides of the equation to obtain:
$\require{cancel}70 \cdot \frac{1}{14}(3x-2)=70 \cdot \frac{x+10}{10}
\\5\cancel{70} \cdot \frac{1}{\cancel{14}}(3x-2)=7\cancel{70} \cdot \frac{x+10}{\cancel{10}}
\\5(3x-2)=7(x+10)$
Distribute $5$ and $7$ to obtain:
$5(3x)-5(2)=7(x) + 7(10)
\\15x-10=7x+70$
Subtract $7x$ and add $10$ on both sides of the equation, then combine like terms to obtain:
$15x-10-7x+10=7x+70-7x+10
\\8x=80$
Divide $8$ to both sides:
$\dfrac{8x}{8} = \dfrac{80}{8}
\\x=10$