Question

c) \\(\frac{1}{2x} + \frac{3}{6} = \frac{5}{3}\\)

Explanation:

Step1: Simplify constant terms

Subtract $\frac{3}{6}$ from both sides.
$\frac{1}{2x} = \frac{5}{3} - \frac{3}{6}$
Simplify $\frac{3}{6}=\frac{1}{2}$, so $\frac{5}{3}-\frac{1}{2}=\frac{10 - 3}{6}=\frac{7}{6}$
Result: $\frac{1}{2x} = \frac{7}{6}$

Step2: Cross-multiply to solve for $x$

Cross multiply the fractions.
$7\times2x = 1\times6$
Simplify left side: $14x = 6$

Step3: Isolate $x$

Divide both sides by 14.
$x = \frac{6}{14} = \frac{3}{7}$

Answer:

$x=\frac{3}{7}$