Question

how many solutions does this equation have?
6(2k + 1) = 12k + 1
no solution
one solution
two solutions
infinitely many solutions

Explanation:

Step1: Expand left-hand side

$6(2k + 1) = 12k + 6$

Step2: Rewrite original equation

$12k + 6 = 12k + 1$

Step3: Subtract $12k$ from both sides

$6 = 1$

Step4: Analyze the resulting statement

This is a false contradiction, so no value of $k$ can satisfy the equation.

Answer:

no solution