#### Answer

$$x=-\frac{12}{17}$$

#### Work Step by Step

$$\frac{4x-1}{10} = \frac{5x+2}{4}$$
Perform cross multiplication by multiplying the numerator of the left-hand fraction by the denominator of the right-hand fraction, and by multiplying the numerator of the right-hand fraction by the denominator of the left-hand fraction:
$$(4x-1)\cdot 4 = (5x+2)\cdot 10$$
Expand $(4x-1)\cdot 4$:
$$=16x-4$$
Expand $(5x+2)\cdot 10$:
$$=50x+20$$
Rewrite the equation:
$$16x-4 = 50x+20$$
Add $4$ to both sides:
$$16x-4+4 = 50x+20+4$$
$$16x = 50x+24$$
Subtract $50x$ from both sides:
$$16x-50x = 50x-50x+24$$
$$-34x = 24$$
Divide both sides by $-34$:
$$\frac{34x}{-34} = \frac{24}{-34}$$
$$x = -\frac{24}{34}$$ or $$x = -\frac{12}{17}$$