Question

solve the following equation. check your solution.
19(v + 2) - 3v = 4(4v + 2) - 12

select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the solution is v = \boxed{}. (type an integer or a fraction.)
b. the solution is all real numbers.
c. there is no solution.

Explanation:

Step1: Expand both sides

Expand \(19(v + 2)-3v\) to get \(19v + 38-3v=16v + 38\). Expand \(4(4v + 2)-12\) to get \(16v+8 - 12=16v - 4\). Now the equation is \(16v + 38=16v - 4\).

Step2: Subtract \(16v\) from both sides

Subtract \(16v\) from both sides: \(16v - 16v+38=16v - 16v - 4\), which simplifies to \(38=-4\). This is a false statement.

Answer:

C. There is no solution.