Question

solve the linear equation.
\\(\frac{y}{5}+\frac{1}{2}=6y\\)
select the correct choice below and, if necessary, fill in the answer box to c
\\(\bigcirc\\) a. \\(y = \square\\) (type an integer or a simplified fraction.)
\\(\bigcirc\\) b. the solution is all real numbers.
\\(\bigcirc\\) c. there is no solution.

Explanation:

Step1: Eliminate denominators

Multiply each term by 10 (LCM of 5 and 2) to eliminate fractions:
$$10\times\frac{y}{5} + 10\times\frac{1}{2} = 10\times6y$$
Simplify:
$$2y + 5 = 60y$$

Step2: Isolate variable terms

Subtract \(2y\) from both sides:
$$5 = 60y - 2y$$
Simplify:
$$5 = 58y$$

Step3: Solve for \(y\)

Divide both sides by 58:
$$y = \frac{5}{58}$$

Answer:

A. \( y = \frac{5}{58} \)