Question

how many solutions does the following equation have: 3(n + 1) = 3n + 1 one solution infinite solutions no solutic

Explanation:

Step1: Expand the left side

Expand \( 3(n + 1) \) using the distributive property \( a(b + c)=ab+ac \), we get \( 3n + 3 \). So the equation becomes \( 3n + 3 = 3n + 1 \).

Step2: Subtract \( 3n \) from both sides

Subtract \( 3n \) from both sides of the equation \( 3n + 3 = 3n + 1 \), we have \( 3n - 3n + 3 = 3n - 3n + 1 \), which simplifies to \( 3 = 1 \).

Step3: Analyze the result

The statement \( 3 = 1 \) is false. When we end up with a false statement after simplifying an equation, it means the equation has no solution.

Answer:

No solution