Question

Which of the following equations have no solution?

a. 6x + 1 = 3(2x – 4)
b. 2 - 5x = 7x – 12
c. 4(3 – x) = 2(6 - 2x)
d. 5(x + 2) = 2(x – 4)
e. -4(x + 3) = 4(x - 1)

Answer 1

The equation a. 6x + 1 = 3(2x - 4) has no solution, while the other equations have solutions.

Step-by-step explanation:

The equation 6x + 1 = 3(2x - 4) can be simplified as follows:

1. 6x + 1 = 6x - 12
2. 1 = -12

Since the equation is contradictory, it has no solution.

Similarly, the equation 2 - 5x = 7x - 12 can be simplified as follows:

1. 2 + 12 = 7x + 5x
2. 14 = 12x
3. x = 14/12

The solution x = 7/6 is a valid solution, so this equation does have a solution.

For the remaining equations, it can be observed that they can be simplified as:

1. 4(3 - x) = 2(6 - 2x) simplifies to 12 - 4x = 12 - 4x, which is an identity with infinitely many solutions.
2. 5(x + 2) = 2(x - 4) simplifies to 5x + 10 = 2x - 8, which can be further simplified as 3x = -18, and x = -6. Hence, this equation does have a solution.
3. -4(x + 3) = 4(x - 1) simplifies to -4x - 12 = 4x - 4, which can be further simplified as -12 = 8x, and x = -3/2. This equation does have a solution.

In conclusion, the equations that have no solution are: a. 6x + 1 = 3(2x - 4).