Question

solve the equation, and check your solution.
2(6s + 4) - 6s = 2(3s + 6) - 14

select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the solution set is { }. (simplify your answer.)
b. the solution set is {all real numbers}.
c. the solution set is ∅.

Explanation:

Step1: Expand both sides

Left side: \(2(6s + 4)-6s = 12s + 8 - 6s\)
Right side: \(2(3s + 6)-14 = 6s + 12 - 14\)

Step2: Simplify both sides

Left side: \(12s + 8 - 6s = 6s + 8\)
Right side: \(6s + 12 - 14 = 6s - 2\)

Step3: Set up the equation and solve

We have \(6s + 8 = 6s - 2\)
Subtract \(6s\) from both sides: \(8=-2\)
This is a contradiction, so there is no solution.

Answer:

C. The solution set is \(\varnothing\)