Question

1. \\(\frac{x}{3} - \frac{7x}{12} = \frac{2}{3}\\)

Explanation:

Step1: Find common denominator

The denominators are 3 and 12, so the common denominator is 12. Multiply each term by 12 to eliminate fractions:
$$12\times\frac{x}{3}-12\times\frac{7x}{12}=12\times\frac{2}{3}$$
Simplify each term: $4x - 7x = 8$

Step2: Combine like terms

Combine the $x$ terms: $4x - 7x = -3x$, so the equation becomes $-3x = 8$

Step3: Solve for x

Divide both sides by -3: $x = \frac{8}{-3}=-\frac{8}{3}$

Answer:

$x = -\frac{8}{3}$