Final answer:
Five equivalent equations to the original equation 2x+4=x-4 are created by applying identical mathematical operations to both sides of the original equation, resulting in new, yet equivalent, forms.
Step-by-step explanation:
The student is asking for 5 different equations that are equivalent to the original equation 2x+4=x-4. We can create equivalent equations by performing the same mathematical operations on both sides of the equation. Here are five equivalent equations:
- 1. 2x = x - 8 &
- 2. x = -12 &
- 3. 3x + 4 = -4 &
- 4. 4x + 8 = 2x - 8 &
- 5. x/2 + 2 = (x - 4)/2
Each equation is derived by algebraically manipulating the original equation using operations such as subtraction, division, or multiplication. To obtain these equations, we must ensure that the same operation is applied to both sides, which keeps the equations equivalent to the original.