Question

solve for u.
\\(\frac{u - 3}{6} + \frac{6u - 3}{2} = 17\\)
simplify your answer as much as possible.
\\(u = \boxed{}\\)

Explanation:

Step1: Eliminate denominators

Multiply each term by 6 (the least common denominator of 6 and 2) to get rid of the fractions:
$$6\times\frac{u - 3}{6}+6\times\frac{6u - 3}{2}=6\times17$$
Simplify each term:
$$u - 3 + 3(6u - 3)=102$$

Step2: Expand and simplify

Expand the left - hand side:
$$u - 3+18u - 9 = 102$$
Combine like terms:
$$(u + 18u)+(-3-9)=102$$
$$19u-12 = 102$$

Step3: Solve for u

Add 12 to both sides of the equation:
$$19u-12 + 12=102 + 12$$
$$19u=114$$
Divide both sides by 19:
$$u=\frac{114}{19}$$
Simplify the fraction:
$$u = 6$$

Answer:

\(u = 6\)