Question

solve the equation.
38 + 3y - 16 = 13y - 13 - 5y
select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the solution is y = . (type an integer or a fraction.)
b. the solution is all real numbers.
c. there is no solution.

Explanation:

Step1: Simplify both sides

Simplify left side: \(38 + 3y - 16 = 22 + 3y\)
Simplify right side: \(13y - 13 - 5y = 8y - 13\)
Equation becomes: \(22 + 3y = 8y - 13\)

Step2: Isolate variable \(y\)

Subtract \(3y\) from both sides: \(22 = 5y - 13\)
Add \(13\) to both sides: \(35 = 5y\)

Step3: Solve for \(y\)

Divide both sides by \(5\): \(y = 7\)

Answer:

A. The solution is \(y = 7\).