Question

solve the equation. express numbers as integers or simplified fractions.\\(\frac{5n - 3}{4} + \frac{5 - 3n}{2} = \frac{3 - 4n}{6}\\)\
the solution set is \\(\\{\\ \\}\\).

Explanation:

Step1: Eliminate denominators (LCM=12)

Multiply each term by 12:
$$12\times\frac{5n-3}{4} + 12\times\frac{5-3n}{2} = 12\times\frac{3-4n}{6}$$
Simplify to:
$$3(5n-3) + 6(5-3n) = 2(3-4n)$$

Step2: Expand all parentheses

$$15n - 9 + 30 - 18n = 6 - 8n$$

Step3: Combine like terms

$$-3n + 21 = 6 - 8n$$

Step4: Isolate n terms

Add $8n$ to both sides:
$$5n + 21 = 6$$

Step5: Solve for n

Subtract 21, then divide by 5:
$$5n = 6 - 21 = -15$$
$$n = \frac{-15}{5} = -3$$

Answer:

$\{-3\}$