Question

Which equation has no solution?

a) (4(x + 3) + 2x = 6(x + 2))
b) (5(3 + 2x) = x + 3(x + 1))
c) (5(x + 3) + x = 4(x + 3) + 3)
d) (4 + 6(2 + x) = 2(3x + 8))

Answer 1

The equation that has no solution is option (a) (4(x + 3) + 2x = 6(x + 2)).

Step-by-step explanation:

The equation that has no solution is option a) (4(x + 3) + 2x = 6(x + 2)). To determine this, we need to simplify each equation and see if the variables cancel out and result in a false statement. In option a), the left side becomes 4x + 12 + 2x, and the right side becomes 6x + 12. Simplifying further, we have 6x + 12 = 6x + 12. Since the variables cancel out and both sides are equal, this equation has an infinite number of solutions, not no solution.

Similarly, if we simplify options b), c), and d), we will find that they all result in true statements, indicating that they have a solution. Therefore, the correct answer is option a) which has no solution.