HSA.REI.A.2 math practice. Learn by doing.

Cross-multiply to clear the fraction: $2(4x - y) = 3(x + 2y)$, so $8x - 2y = 3x + 6y$. Collect like terms to get $5x = 8y$. Divide both sides by $y$, then by $5$, to obtain $\dfrac{x}{y} = \dfrac{8}{5}\textsf{.}$

For $x \neq -7$, the factor $x+7$ cancels, giving $x+1 = -2$, so $x = -3\textsf{.}$

Cross-multiply to clear the fraction: $5(x + 4y) = 3(2x + y)$, so $5x + 20y = 6x + 3y$. Collect like terms to get $x = 17y$. Divide both sides by $y$ to obtain $\dfrac{x}{y} = 17\textsf{.}$

For $x \neq 3$, the factor $x-3$ cancels, giving $x+5 = 12$, so $x = 7\textsf{.}$

Cross-multiply to clear the fraction: $4(x - 2y) = 1(3x + y)$, so $4x - 8y = 3x + y$. Collect like terms to get $x = 9y$. Divide both sides by $y$ to obtain $\dfrac{x}{y} = 9\textsf{.}$

For $x \neq -2$, the factor $x+2$ cancels, giving $x-8 = 5$, so $x = 13\textsf{.}$

Cross-multiply to clear the fraction: $5(4x - 3y) = 2(x + y)$, so $20x - 15y = 2x + 2y$. Collect like terms to get $18x = 17y$. Divide both sides by $y$, then by $18$, to obtain $\dfrac{x}{y} = \dfrac{17}{18}\textsf{.}$

Factor the numerator: $x^{2} - 25 = (x-5)(x+5)$. For $x \neq -5$, the factor $x+5$ cancels, giving $x-5 = 2$, so $x = 7\textsf{.}$