Question

determine whether the equation is a conditional equation, an identity, or a contradiction. give the solution set.
6(v + 1) - 2v = 2(2v + 2) - 8
is the equation a conditional equation, an identity, or a contradiction?
a. contradiction
b. conditional equation
c. identity
select the correct choice below and fill in any answer boxes present in your choice.
a. the solution set is { } (type an integer or a fraction. use a comma to separate answers as needed)
b. the solution is all real numbers
c. the solution is the empty set

Explanation:

Step1: Expand both sides

Expand \(6(v + 1)-2v\): \(6v + 6 - 2v=4v + 6\)
Expand \(2(2v + 2)-8\): \(4v + 4 - 8 = 4v - 4\)

Step2: Simplify and compare

Now the equation is \(4v + 6 = 4v - 4\). Subtract \(4v\) from both sides: \(6=-4\), which is false.

Answer:

The equation is a contradiction (Option A). The solution set is \(\{\}\) (empty set).