Which equation has a different solution than the rest?(1 point)

Question

Responses

16x=64
16x equals 64

−12x=48
negative 12x equals 48

x−2=2
Start Fraction x over negative 2 equals 2

x4=−1

Answer 1

Let's solve each equation to determine which one has a different solution:

1. For the equation \(16x = 64\): \[ x = \frac{64}{16} = 4 \]

2. For the equation \(-12x = 48\): \[ x = \frac{48}{-12} = -4 \]

3. For the equation \(x - 2 = 2\): \[ x = 2 + 2 = 4 \]

4. For the equation \(x^4 = -1\): The equation \(x^4 = -1\) has no real solutions because the fourth power of a real number cannot be negative. Therefore, it would have solutions in the complex number system, specifically \(x = \pm i\) (where \(i\) is the imaginary unit).

Now, summarizing the solutions:

• \(16x = 64\) gives \(x = 4\)
• \(-12x = 48\) gives \(x = -4\)
• \(x - 2 = 2\) gives \(x = 4\)
• \(x^4 = -1\) has no real solutions (\(x = \pm i\))

The equation \(x^4 = -1\) has a different solution (in the complex plane) compared to the others, which yield real solutions.

Thus, the answer is \(x^4 = -1\).