Question

1. \\(\frac{3}{2}x - \frac{2}{3}x = 2\\)

Explanation:

Step1: Find common denominator

The common denominator of 2 and 3 is 6. Rewrite the terms:
$\frac{9}{6}x - \frac{4}{6}x = 2$

Step2: Combine like terms

Subtract the fractions:
$\frac{9x - 4x}{6} = 2$
$\frac{5}{6}x = 2$

Step3: Solve for x

Multiply both sides by $\frac{6}{5}$:
$x = 2 \times \frac{6}{5}$

Answer:

$x = \frac{12}{5}$