Question

Question Which of the following equations has a solution different from the rest? (1 point)

1/2x - 3 = 1/2
- 1/7x - 3/4 = 1/4
-0.35x - 0.52 = 1.93
3/4x + 5 = -1/4

Answer 1

All equations except for the first have a solution of x = -7. The first equation has a different solution, with x = 7. Therefore, the equation 1/2x - 3 = 1/2 has a different solution from the others.

Step-by-step explanation:

The question asks which of the given equations has a solution different from the rest. To find the solution to each of the equations, we need to isolate the variable x on one side of the equation.

For the equation 1/2x - 3 = 1/2, we add 3 to both sides to get 1/2x = 3.5 and then multiply both sides by 2 to solve for x, which gives us x = 7.

In the equation -1/7x - 3/4 = 1/4, we start by adding 3/4 to both sides resulting in -1/7x = 1. Multiplying both sides by -7 gives us x = -7.

For -0.35x - 0.52 = 1.93, we add 0.52 to both sides to obtain -0.35x = 2.45. Dividing by -0.35 provides the solution x = -7.

The last equation 3/4x + 5 = -1/4 requires subtracting 5 from both sides to get 3/4x = -21/4. Multiplying by 4/3 yields x = -7.

All equations except for the first result in x = -7. Therefore, the first equation, 1/2x - 3 = 1/2, has a solution different from the rest which is x = 7.

Answer 2

None of the given equations have a solution different from the rest.

Step-by-step explanation:

In order to determine which equation has a solution different from the rest, we need to solve each equation and see if there are any extraneous solutions. Let's solve each equation one by one:

1. 1/2x - 3 = 1/2: Adding 3 to both sides, we get 1/2x = 7/2. Multiplying both sides by 2, we get x = 7 which is a valid solution.
2. -1/7x - 3/4 = 1/4: Adding 3/4 to both sides, we get -1/7x = 1/2. Multiplying both sides by -7, we get x = -7/2 which is a valid solution.
3. -0.35x - 0.52 = 1.93: Adding 0.52 to both sides, we get -0.35x = 2.45. Dividing both sides by -0.35, we get x ≈ -7 which is a valid solution.
4. 3/4x + 5 = -1/4: Subtracting 5 from both sides, we get 3/4x = -5 1/4. Multiplying both sides by 4/3, we get x ≈ -7/3 which is a valid solution.

All of the equations have valid solutions, so none of them have a solution different from the rest.