## Intermediate Algebra for College Students (7th Edition)

$$x=-\frac{12}{17}$$
$$\frac{4x-1}{10} = \frac{5x+2}{4}$$ 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 $$x = -\frac{12}{17}$$