Solve the linear equation: (2x)/(3) − 3 = (5)/(2)x + 6

Subtract $\frac{5}{2}x$ from both sides:

$$\frac{2x}{3} - \frac{5}{2}x - 3 = 6$$

Add 3 to both sides:

$$\frac{2x}{3} - \frac{5}{2}x = 6 + 3$$ $$\frac{2x}{3} - \frac{5x}{2} = 9$$

The least common multiple (LCM) of 3 and 2 is 6.
Rewrite the fractions with the common denominator:

$$\frac{2x \cdot 2}{3 \cdot 2} - \frac{5x \cdot 3}{2 \cdot 3} = 9$$ $$\frac{4x}{6} - \frac{15x}{6} = 9$$

$$\frac{4x - 15x}{6} = 9$$ $$\frac{-11x}{6} = 9$$

Multiply both sides by 6:

$$-11x = 9 \cdot 6$$ $$-11x = 54$$

Divide both sides by -11:

$$x = \frac{54}{-11}$$ $$x = -\frac{54}{11}$$

The final answer is $-\frac{54}{11}$.