Solve the following equations.

1. $\dfrac{8x - 3}{3x} = 2$

$\dfrac{8x - 3}{3x} = 2$
$\Rightarrow \dfrac{8x}{3x} - \dfrac{3}{3x} = 2$
$\Rightarrow \dfrac{8}{3} - \dfrac{1}{x} = 2$
$\Rightarrow \dfrac{8}{3} - 2 = \dfrac{1}{x}$
$\Rightarrow \dfrac{8-6}{3} = \dfrac{1}{x}$
$\Rightarrow \dfrac{2}{3} = \dfrac{1}{x}$
$\Rightarrow x = \dfrac{3}{2}$

2. $\dfrac{9x}{7-6x} = 15$

$9x = 15(7-6x)$
$\Rightarrow 9x = 105 - 90x$
$\Rightarrow 9x + 90x = 105$
$\Rightarrow 99x = 105$
$\Rightarrow x = \dfrac{105}{99}$
$\Rightarrow x = \dfrac{35}{33}$

3. $\dfrac{z}{z+15} = \dfrac{4}{9}$

$z = \dfrac{4}{9} (z+15)$
$\Rightarrow 9z = 4(z+15)$
$\Rightarrow 9z = 4z + 60$
$\Rightarrow 9z - 4z = 60$
$\Rightarrow 5z = 60$
$\Rightarrow z = 12$

4. $\dfrac{3y+4}{2-6y} = -\dfrac{2}{5}$

$3y + 4 = -\dfrac{2}{5} (2-6y)$
$\Rightarrow 5(3y+4) = -2(2-6y)$
$\Rightarrow 15y + 20 = -4 + 12y$
$\Rightarrow 15y - 12y = -4 - 20$
$\Rightarrow 3y = -24$
$\Rightarrow y = -8$

5. $\dfrac{7y+4}{y+2} = -\dfrac{4}{3}$

$7y + 4 = -\dfrac{4}{3} (y+2)$
$\Rightarrow 3(7y+4) = -4(y+2)$
$\Rightarrow 21y + 12 = -4y - 8$
$\Rightarrow 21y + 4y = -8 - 12$
$\Rightarrow 25y = -20$
$\Rightarrow y = -\dfrac{20}{25}$
$\Rightarrow y = -\dfrac{4}{5}$

1. $\dfrac{8x - 3}{3x} = 2$

$\dfrac{8x - 3}{3x} = 2$
$\Rightarrow \dfrac{8x}{3x} - \dfrac{3}{3x} = 2$
$\Rightarrow \dfrac{8}{3} - \dfrac{1}{x} = 2$
$\Rightarrow \dfrac{8}{3} - 2 = \dfrac{1}{x}$
$\Rightarrow \dfrac{8-6}{3} = \dfrac{1}{x}$
$\Rightarrow \dfrac{2}{3} = \dfrac{1}{x}$
$\Rightarrow x = \dfrac{3}{2}$

2. $\dfrac{9x}{7-6x} = 15$

$9x = 15(7-6x)$
$\Rightarrow 9x = 105 - 90x$
$\Rightarrow 9x + 90x = 105$
$\Rightarrow 99x = 105$
$\Rightarrow x = \dfrac{105}{99}$
$\Rightarrow x = \dfrac{35}{33}$

3. $\dfrac{z}{z+15} = \dfrac{4}{9}$

$z = \dfrac{4}{9} (z+15)$
$\Rightarrow 9z = 4(z+15)$
$\Rightarrow 9z = 4z + 60$
$\Rightarrow 9z - 4z = 60$
$\Rightarrow 5z = 60$
$\Rightarrow z = 12$

4. $\dfrac{3y+4}{2-6y} = -\dfrac{2}{5}$

$3y + 4 = -\dfrac{2}{5} (2-6y)$
$\Rightarrow 5(3y+4) = -2(2-6y)$
$\Rightarrow 15y + 20 = -4 + 12y$
$\Rightarrow 15y - 12y = -4 - 20$
$\Rightarrow 3y = -24$
$\Rightarrow y = -8$

5. $\dfrac{7y+4}{y+2} = -\dfrac{4}{3}$

$7y + 4 = -\dfrac{4}{3} (y+2)$
$\Rightarrow 3(7y+4) = -4(y+2)$
$\Rightarrow 21y + 12 = -4y - 8$
$\Rightarrow 21y + 4y = -8 - 12$
$\Rightarrow 25y = -20$
$\Rightarrow y = -\dfrac{20}{25}$
$\Rightarrow y = -\dfrac{4}{5}$