Question

Solve the equation 3(x+1) = 3x+1.

a) x = 1
b) x = 2
c) x = 0
d) x = -1

Answer 1

The equation 3(x+1) = 3x+1 simplifies to a false statement (3=1) after subtracting 3x from both sides, which indicates that there is no solution.

Step-by-step explanation:

To solve the equation 3(x+1) = 3x+1, we need to simplify the expression:

1. Begin by distributing the 3 on the left side: 3*x + 3*1 = 3x + 1.
2. This simplifies to 3x + 3 = 3x + 1.
3. Since 3x is on both sides of the equation, we can subtract 3x from both sides, naively simplifying to 3 = 1, which is not true.
4. This shows that the equation has no solution, as the variable x cancels out, leaving a false statement.

So, none of the given options a) x = 1, b) x = 2, c) x = 0, or d) x = -1 is correct. The correct answer is that the equation has no solution.