To find the equation that is equivalent to 4x³ = 64, we need to manipulate the equation to isolate the variable x. Let's go through each option to determine which one is equivalent to the given equation:
1. Option: 2x + 6 = 24
This equation is not equivalent to the given equation. It involves addition and subtraction of terms, whereas the given equation involves exponentiation.
2. Option: 22x + 6 - 26
This equation is not equivalent to the given equation. It involves subtraction and addition of constants, whereas the given equation involves exponentiation and the constant value of 64.
3. Option: 42x + 6 = 4²
This equation is not equivalent to the given equation. It involves multiplication and addition of terms, whereas the given equation involves exponentiation.
4. Option: 4x + 3 = 46
This equation is equivalent to the given equation. By subtracting 3 from both sides of the equation, we can isolate 4x on the left side and get 4x = 43. Dividing both sides by 4, we find x = 10.75.
Therefore, the equation that is equivalent to 4x³ = 64 is 4x + 3 = 46.